Geographical Information Systems and Dynamic Models

Geographical Information Systems and Dynamic Models

Development and application of a prototype spatial modelling language

WPA van Deursen PhD-thesis, may 19, 1995 Faculty of Spatial Sciences University of Utrecht The Netherlands

@1995,2000, WPA van Deursen Oostzeedijk Beneden 23a 3062 VK Rotterdam, The Netherlands [email protected]

This publication is also available in paper form. This publication is part of NGS, Netherlands Geographical Studies. NGS 190 W P A VAN DEURSEN Geographical Information Systems and Dynamic Models; development and application of a prototype spatial modelling language -- Utrecht 1995: Knag/Faculteit Ruimtelijke Wetenschappen Universiteit Utrecht. 206 pp, 44 figs, 8 tabs. ISBN 90-6809-206-5 Dfl 38,00 Publications of this series can be ordered from KNAG / NETHERLANDS GEOGRAPHICAL STUDIES, P.O.Box 80123, 3508 TC Utrecht, The Netherlands (Fax +31 30 253 5523; E-mail [email protected]).

Please refer to this publication as: Van Deursen W.P.A. 1995. Geographical Information Systems and Dynamic Models. Ph.D. thesis, Utrecht University, NGS Publication 190, 198 pp. Electronically available through www.carthago.nl

Please feel free to copy and redistribute this PDF document, provided that no changes are made to the document.

The PCRaster software, which implements the techniques described in this document (although not exactly) is available through www.pcraster.nl

Rotterdam, November 2000 Willem van Deursen, [email protected]

1

INTRODUCTION

1.1 The use of Geographical Information Systems and dynamic models in physical geography, ecology and environmental studies A convenient way to define a Geographical Information System (GIS) is to say that it is a set of computer tools capable of storing, manipulating, analysing and retrieving geographic information [Burrough, 1986; Maguire, 1991]. Several questions arise from this definition. What exactly is geographic information; and what is meant by the sentence 'storing, manipulating and analysing and retrieving geographic information'? Both these questions are the cause of much discussion and research in the GIS society. This thesis will touch upon the first question, and will discuss thoroughly an approach for dynamic modelling with GIS. In this context dynamic modelling can be regarded as a subset of 'manipulating and analysing geographic data'. Geographic information is information that has a geographic attribute, that is, it is linked to some location. We can recognise two main types of geographic information [Goodchild 1992]. The first type relates to the concept of objects, features that can have a certain set of attributes. It is quite convenient to think of objects as being geographically limited in size, and objects are quite often man-made or stem from classification of the world. In contrast to the object-related information, there is the concept of fields. Fields are not geographically limited, but may have different attribute values at different locations. Elevation is an example of a field. The attribute 'metres above sea level' is defined over the total area, but may take different values at different locations. The major discussion in the GIS world about the vector and raster approaches is mainly along the lines of the concept of objects and fields. The second important aspect of the definition of GIS is the capability for manipulating and analysing the geographic information. Manipulating and analysing refer to retrieving data from the geographical database and creating new information by combining this data. The analysis and manipulation are done through commands and functions. A major milestone in the development of GIS capabilities for manipulating and analysing geographic information has been the formulation of Map Algebra and Cartographic Modelling [Tomlin and Berry, 1979; Tomlin, 1983; Berry 1987]. Map Algebra is an integrated set of functions and commands for analysing and manipulating geographic information. The major significance of Map Algebra is that it does not provide ad hoc operations and functions for all possible geographic analyses that could be conceived, but instead provides limited generic functionality, which can be used as primitives for the analysis. By combining operations, Cartographic Modelling allows for more complex analysis. Cartographic Modelling has been successfully applied in fields such as environmental planning, land evaluation, forest management and so on. As the understanding of the processes that govern the development and degradation of landscapes and our environment evolves, so does our need for simulation models which describe these processes. Simulation models are simplifications of the real world, sets of rules that describe our perspective on the processes. The use of simulation models serves several goals. One of the most important goals is that the models can be used to assess the development or the reaction of our environment in response to human interactions. By using simulation models we can assess land degradation due to watershed management [De Roo, 1993; De Jong, 1994], increased river discharge as a result of climate change [Kwadijk, 1993], or changes in ecosystems due to increased atmospheric deposition of nitrogen [Van Deursen and Heil, 1993]. Another major goal for using simulation models is that they increase the insight and knowledge that we have on the system. Applying various sets of input parameters when using the simulation model may provide insight in the reaction and sensitivity of the processes that are modelled. Simulation models can be used to assess the effects of management options before the options are tried out in the real landscape. This increases understanding of the real world without causing irreversible damage to the landscape. Recently, researchers in numerous sciences are developing or using environmental process models which use spatial distributed data, or geographic information. This information is quite often available in GIS. The natural evolution for both GIS and simulation models is a tighter integration between GIS and these models, thus aiming for the best of both worlds. Cartographic Modelling covers quite a long stretch of the road towards a tighter integration of GIS and (static) models. However, it falls short on the aspects where dynamic models and more complex algorithms are involved.

1.2

Objectives of the thesis

This research deals with approaches and concepts for a fruitful integration of dynamic models and GIS. The first chapters give an overview of the current state of GIS, the characteristics of dynamic models and the research in the area of linking dynamic models and GIS. Next, the thesis describes the concepts behind an integration of dynamic models and GIS. This section continues with an overview of the generic functionality required for an integrated GIS-dynamic model environment and an overview of current state-of-the-art GIS-programs in relation to this required functionality. A prototype GIS for dynamic modelling, called PCRaster, is presented, which has been developed as part of this thesis: it is an operational implementation of the ideas and concepts discussed. The GIS consists of a general purpose GIS and a specific toolbox with modules for dynamic modelling. The third section provides a detailed description of the modules of the new GIS. This section discusses the application of the provided modelling techniques in several problems in physical geography and ecology. The fourth section of the thesis gives an overview of several different case studies. These studies serve as an example of the concepts and techniques described in the thesis. Case studies implementing existing (assumed validated and calibrated) models in the GIS are discussed. This section gives particular emphasis to the capabilities of the system for different applications. The final chapter examines the degree to which this study has provided and tested a prototype integrated GIS for dynamic modelling in environmental studies. The question to be answered in this thesis is • Can we build a general purpose GIS with intrinsic dynamic modelling functionality, which can be used to develop, apply and evaluate models for a large number of environmental processes? This question leads to several research questions to be answered in this study: • What are the advantages and disadvantages of the different techniques available for linking GIS and dynamic models? •

Can we classify the dynamic models currently used for physical geography, ecology and environmental issues into useful sets of approaches and processes?

•

Can we build general purpose tools to match these approaches and processes and are they capable of giving reasonable results for a variety of problems over a wide range of spatial scales?

•

Are these tools sufficiently robust to be given to GIS users who a) are not expert modellers, and/or b) have access to large amounts of quite general data of mixed quality?

•

For what kinds of dynamic modelling do they present a reasonable solution - where do they provide a useful supplement to existing methods?

•

What should be the level of abstraction of these modules?

•

Can we successfully model real-world problems in this GIS environment?

1.3

Inspiration for this research

One major source of inspiration for this research stems from a publication describing a hydrological study carried out in the 1930's. Merill Bernard took the task of using the results of runoff plot experiments to predict the effect of land use on runoff and erosion on a 3 km2 plot [Bernard, 1937; Hjemfelt and Amerman, 1980]. Bernard's description of the problems encountered when trying to reach the objectives of the study were:

'Of necessity, the erosion experiment stations were limited to small farm units of about 200 acres. Further limitations in funds and personnel reduced the size of the individual investigations to areas ranging in size from a fraction of an acre to 4 or 5 acres. On these experimental areas, a number of rainfall and runoff observations have been made, many of which show marked contrasts in runoff and soil loss under various surface treatments and cover. The usefulness of these data is definitely limited, for the following reasons: First, the period is not sufficiently long to have embraced the full range of all factors influencing the result; second, there are comparatively few cases in which runoff has been observed under unusually excessive rainfall; and third, the experimental areas are so small that the results cannot be considered as having areal significance. It is the purpose of this paper to present and demonstrate a method which, in a practical degree, may be used to overcome the latter limitation'. It is interesting to notice that the problems encountered by hydrologists in the 1930's are still the main issues that bothered scientific modelling in the 1990's. Bernard continues: 'Obviously, a result obtained on seven-tenth of an acre or 7 acres cannot be extrapolated to 700 acres by means of simple multiplication. It is believed, however, that resorting only to wellestablished hydraulic assumptions, a method of combining and routing flow makes it possible the projection of the results on these small areas to larger areas in the form of natural watersheds'. A model was developed, by subdividing the basin '... into elemental units which are comparable in size to the observational areas found on the erosion experimental stations. It then develops the hydrograph of flow at various points on the stream system and at the outlet of the watershed by combining and routing the flow from each of the elemental units, assigning to each the result of an actual rainfall. This, in effect, assumes that the conditions on the elemental unit, and those on the experimental area whose hydrograph it has been assigned, are identical'. 'This study now proposes to determine, in the form of hydrographs of flow at the outlet of the 730 acre watershed, the effect on the hydrograph of progressively passing from the assumption that the entire watershed is covered by sod,... to that under which is it entirely covered by the corn crop... The procedure is to develop the hydrographs at the outlet of each of the laterals, after which the flow is assembled throughout the length of the main channels. After initial hydrographs have been assigned to the elemental units, routing schedules are prepared for each of the laterals. While the combination and routing could be done analytically by an elaborate system of listing and tabulation, it is believed that the graphical method proposed is far more economical in both time and paper. It has been found best to plot the initial hydrographs, as well as their combinations, on transparent coordinate paper, using a sharp, hard pencil...' Bernard's acknowledges: '...his indebtedness to Ivan Bloch, Associate Engineer, of the Rural Electrification Administration, for technical assistance of the highest order. Mr Bloch assisted in the development of the method described and prepared many of the graphs and figures entailing several hundred hydrograph translations.' If only GIS could have made Merill Bernard's and Ivan Bloch's task a little bit easier...

2

ENVIRONMENTAL MODELS AND GIS 'What do you consider the largest map that would be really useful?' 'About six inches to the mile.' 'Only six inches!' exclaimed Mein Herr. 'We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the greatest idea of all! We actually made a map on the scale of a mile to the mile!' 'Have you used it much?' I enquired. 'It has never been spread out yet,' said Main Herr: 'the farmers objected; they said it would cover the whole country and shut out the sunlight! So now we use the country itself as its own map.' (Lewis Caroll, Sylvie and Bruno Concluded)

2.1

Introduction GIS

As noted in chapter 1, GIS can be defined as a system designed for storing, retrieving and manipulating geographical data [Burrough, 1986]. Several other authors give similar definitions [Tomlin, 1990; Dueker, 1979; Ozemy et al. 1981; Smith et al., 1987; DoE, 1987; Parker, 1988; Maguire, 1991]. As defined above, GIS is a broad and very unspecific venture in which many disciplines participate. This definition is not specific enough to accurately define the field and scope of GIS. Several computer programs do actually use, store and manipulate geographical data, but are generally not considered GIS systems. Examples are distributed hydrologic models and computer simulation models for ecology and environmental issues. An important aspect of GIS is that it is a collection of generic tools [Berry, 1987; Tomlin, 1983], designed not for specified manipulations of geographic data, but for general purposes. Again, this is not a very useful definition: what is regarded as a general purpose tool in one study can be very specific for the next. Considering the field of hydrology, a collection of computer programs for hydrologic modelling which includes MODFLOW, SHE and ANSWERS can be regarded as a very generic toolkit for an environmental impact study related to hydrological issues. On the other hand, this same collection of models is not general enough to be used in environmental impact studies related to air pollution problems. The same line of reasoning applies to GIS. For some studies GIS has just the right tools to answer all the problems that might arise, but in other, very similar problems, GIS may prove to be very inefficient, only capable of handling the very trivial parts of the problem. The above may yield the conclusion that there is no good definition for GIS, and that several arguments can be given to define every computer program related to geographic data as GIS. In this research we will stick to the definition as given above, but interpret this definition in a very loose way. If we consider GIS as a system designed for manipulating geographic information, we come to a much more important question: how do we want to manipulate geographic data? Just as the fields of geography can be divided into human and physical geography, geomorphology and urban geography and so on, applications of GIS can be found in many disciplines. In recent years there have been many conferences, starting with the general ones on GIS (EGIS etcetera), but increasingly more related to GIS and one particular discipline (HydroGIS, GIS and Coastal Management, Environmental Modelling and GIS). Besides this growth of applications in different disciplines, the (ongoing) development of GIS has given rise to fundamental discussions about the way we want to be able to handle, manipulate and store the spatial data. Apart from being just a tool that helps doing the things we have always done more efficiently, GIS has been a major trigger for a large number of more fundamental theories about structuring geographic information and the links with 'real world' applications and problems. For the analysis of the elements of a GIS, Nyerges [1993] recognizes three perspectives: • a functional perspective concerning what applications a GIS is used for, the nature of GIS use; • a procedural perspective concerning how a GIS works with regard to the various steps in the process to perform this work, the nature of GIS flow; and • a structural perspective concerning how GIS is put together with regard to various components, the nature of GIS architecture.

In addition to these perspectives, an important one may be added: • a conceptual perspective concerning to way a GIS can be used to model the real world. Within the framework of this research, the functional perspective is limited to the applications of GIS for dynamic modelling in environmental applications. This excludes many GIS applications in other fields. In human geography, transport network analysis, cadastral applications and several other fields, large amounts of resources are allocated to research and applications, but only minor attention will be paid to these subjects in this report. The functional perspective of this research is discussed in more detail discussed in section 2.3. The procedural perspective is concerned with the infrastructure of the organisation in which a certain application has to be implemented, and is beyond the scope of this research. The structural perspective is related to the hardware and software of the GIS. It is the design of the software that is responsible for the ease of use, the feasibility of the GIS system to be used in certain applications and the ability of implementation of a certain concept in GIS. As such, the structural design and architecture of GIS play a very important role in the discussion of linking GIS and environmental models, and are discussed more extensively in section 2.2, chapter 3 and chapter 4. The idea that GIS should be used to model the real world is gaining more and more attention. It strongly relates to the functional perspective, since for different applications we may adapt different concepts of 'reality'. Concepts of how to model environmental processes are major topics of section 2.2, chapter 3 and chapter 4.

2.2

Architecture, structures and design of GIS

The structural perspective of analysing GIS is concerned with the methods of how the GIS is put together with regard to various components. The architecture of the GIS determines the combination and integration of the various components. The general architecture of a GIS can be divided into three major components: • database; • analytical engine; and • input, output and user interface. The design of the database is responsible for the way in which the GIS stores the model of the real world. The alternatives for this design and the consequences of choosing the different alternatives are discussed in more detail in section 2.2.1. The analytical engine is the part of GIS that is responsible for the manipulation and transformation of the data. It is this part that is responsible for the analytical capabilities of the system, and as such very important for the possible applications of GIS in environmental studies and dynamic modelling. This part is discussed in more detail in section 2.2.2. The input and output part of the system provides the means to store data into the system and to retrieve data out of the database. A number of important tasks, including digitizing and plotting, interface to other systems, and the user interface are part of this component. The design of the user interface does not determine what can be done with the system, it is only responsible for the ease with which certain tasks can be accomplished. The input, output and user interface are discussed in section 2.2.3.

2.2.1 The database design and its significance The architecture of the data management subsystem determines the design of the descriptive constructs used for data storage. As such, it is the fundamental mechanism for determining the nature of data representation as presented to applications, whether these are integrated functions in GIS or models linked to GIS. The architecture of the subsystem is based on the types of data models used. A data model determines the constructs for storage, the operations for manipulation and the integrity constraints for controlling the validity of data to be stored [Nyerges, 1993].

In the current generation of GIS two highly complementary methods of representation and storage are responsible for the storage and management of data. These two different methods, the vector and the raster structure, are responsible for the distinction of two major families of GIS design and capabilities. Burrough [1986] gives an overview of the advantages and disadvantages of the different systems. An implication of the choice of data representation is that it has a large influence on the functionality of the GIS system. Several operations that are very efficiently implemented in raster GIS are difficult to carry out in vector GIS and vice versa. Recent trends in GIS development try to deal with this problem by implementing so-called hybrid systems. These systems offer both raster and vector storage mechanism and analysis capabilities, and offer a number of conversion routines to convert data between the two data structures. Even in these hybrid systems, the data model is structured around the implementation of the data storage (how do we store data), instead of the nature of the entities (what do we want to store). Current raster and vector based systems (and hybrid systems) emphasize technical details of the data structure. The structure, capacities and incapabilities of these systems are highly determined by this technical detail of data storage. Although it is not yet common practice, it should be the type and nature of the spatial entities that determines the structuring and capabilities of the system. Section 3.3 and chapter 4 discuss this issue in more detail. The prototype GIS PCRaster as presented in chapter 4 implements a system that is structured based on characteristics of the entities to be stored, and pays less attention towards the technical details of data structures for storing data.

2.2.2 The analytical engine The analytical engine is the part of GIS that is responsible for the manipulation and analysis of the spatial data. A good overview of the capabilities and analytical possibilities of the GIS is given in Burrough [1986], Tomlin [1983, 1990] and Berry [1987]. Current analytical capabilities of GIS are highly related to the structure of the database used. The family of raster GIS (MAP-family, Erdas, Idrisi, Grass, Ilwis) is evaluated as having a large analytical power, whereas vector GIS (ArcInfo, Genamap) is thought to be superior for database manipulation such as retrieval and combination of attributes. These vector systems are more favourable for manipulating attributes of (static) objects and transport and network analysis, but it is because of the superior analytical power of raster GIS that these systems are used predominantly for integration with environmental process models. Analysis is done through commands or functions on existing digital maps (overlays) resulting in new overlays. There are many different functions or commands used for the analysis, but a structured set of functions and commands for raster GIS is known under the name of 'Map Algebra'. The processing operations on raster map layers are based on the set of cells in the input grid(s) that participate in the computation of a value for a cell in the output grid: operations are classified as [Tomlin, 1990; Gao et al., 1993]: • per cell or local; • per neighbourhood or focal; • per zone or zonal; and • per layer or global. Local operations compute a new value for each location based on values in other map layers at the same location. Focal operations compute new cell values based on existing values, distances and/or directions within its neighbourhood. Zonal functions compute a new value for each location as a function of the existing values from one layer that are contained in zones of another layer. In global operators all cells in the layer participate in the computation of the result. Most systems support a set of analytic functions including arithmetic, trigonometric, exponential, logarithmic, statistical, tabular reclassification and conditional evaluation functions for raster processing. This rich suite of built-in functions, which can be used to generate output layers that form the components of complex models, include functions for multi-source euclidean distance mapping, topographic shading analysis, watershed analysis, weighted distance mapping, surface interpolation, multivariate regression, clustering and classification, visibility analysis and more [Gao et al., 1993]. Currently, this set of built-in functions is very useful for building static models and deriving model parameters from the digital database, but it lacks some functionality necessary to build dynamic models (see sections 2.3 and 2.4).

2.2.3 User interface and Input and Output It is important to realize that the user interface does not provide the analytical functionality to the GIS, but is just a gateway to this functionality. User interfaces can be designed with several criteria in mind. Opposite viewpoints for designing the user interface may be characterised as: • to be used for education and guide the persons through the GIS commands by means of pull down menus and a user-friendly question and answer system to come to the exact formulation of the command; or • to be used for creating script files for batch processing, in which all the possible options and commands have to be remembered and no interaction with the system is provided during the process of entering the commands. Neither design is superior to the other. If the GIS is to be used by non-experts, the first design seems preferable, but for more experienced users the second option yields a faster and more direct way to communicate to the system. If the second option is not available or limited to only a part of the functions of the analytical engine, this limits the possibility for batch processing considerably. Most GIS systems provide user access at different levels, thus providing the novice user with help and explanation, and allow expert users to create scripts and macro language processing. Part of the interface of GIS is the import and export capability. This includes the operations that are used to create the data set (digitizing) and create output (plotting and map production, report production and production of tables and graphs). More important in the scope of this project are the capabilities of the GIS to import and export data to other computer programs, which allow for analysis and processing of data when functionality is needed which is not available in the GIS. As can be concluded from the next sections, this import and export functionality is currently the most frequently used mechanism for the linkage between GIS and environmental models.

2.3

Linking GIS and environmental models

Environmental modelling is an important tool for obtaining quantitative information for planning and evaluating the resources of land and water jointly. The results of such modelling can give us a better understanding of the dynamics of the landscape because they shed light on how processes such as soil erosion or the transport of pollutants can change the landscape. Geographic Information Systems are very suitable for storing, analysing and retrieving the information needed for running the environmental models. GIS can hold many data on the, albeit static, distribution of land attributes that form the control parameters, boundary conditions and input data for the model [Burrough, 1989].

2.3.1 The nature of environmental modelling Mathematical models (as compared to scale models and analogons) range from simple empirical equations such as linear regression equations (response function models) to sets of complex differential equations derived from fundamental physics (physically based models). The major reasons for developing a mathematical model [Moore et al., 1993; Jørgensen, 1988] are: • to assist in the understanding of the system that it is meant to represent, that is, as a tool for hypothesis testing; • to reveal system properties; and • to provide a predictive tool for management. Apart from these objectives, several advantages of the use of models can be listed [DeCoursey, 1991; De Roo, 1993]: • Hypotheses expressed in mathematical terminology can provide a quantitative description and understanding of chemical, biological and hydrological processes. • Mathematical models can provide a conceptual framework that may help pinpoint areas where knowledge is lacking, and might stimulate new ideas and experimental approaches.

• • • • • • • • •

Mathematical models can be a good way of providing a recipe by which research knowledge is made available in an easy-to-use form to the user. The economic benefits of methods suggested by research can often be investigated and highlighted by a model, thus stimulating the adoption of improved methods of prediction. Modelling may lead to less ad hoc experimentation, as models sometimes make it easier to design experiments to answer particular questions, or to discriminate between alternatives. In a system with several components, a model provides a way of bringing together knowledge about the parts, thus giving a coherent view of the behaviour of the whole system. Modelling can help provide strategic and tactical support to a research program, motivating scientists and encouraging collaboration. A model may provide a powerful means of summarizing data, and a method for interpolation and cautious extrapolation. Data are becoming increasingly precise but also more expensive to obtain; a model can sometimes make more thorough use of data (eg. altitude can be used to calculate slope gradient, aspect, curvature, drainage pattern and watershed area). The predictive power of a successful model may be used in many ways: playing 'what if' games in assigning priorities in research and development, management and planning. Models validated by data from experimental areas provide a mechanism to transfer data from study areas to other areas where fewer data may be available.

Mathematical models describe the state and dynamics of a system (the landscape) in a certain (changing or static) setting using mathematical equations. Jørgensen [1988] recognises five components of a mathematical model. The first component is the set of forcing functions or external variables, which are functions or variables of an external nature that influence the state of the system. The second component is the set of state variables, describing the state or condition of the system. The set of mathematical equations is the third component of the model. These equations represent the processes in the system and the relations between the forcing functions and the state variables. The fourth component is the set of coefficients or parameters in the mathematical equations. These parameters are constant within a specific system, and by calibration of these parameters is attempted to find the best accordance between simulated and observed state variables. The fifth component is a set of universal constants, such as the acceleration due to gravity, which is of course not subject to variation and calibration. The construction and application of a model is usually a five step process: • definition of the problem; • definition of concepts and choosing or developing a model; • gathering data; • calibration and validation of the model; and • application of the model. Although this may seem a list of sequential steps, usually modelling should be considered an iterative process. When the model in the first instance has been verified, validated and calibrated, new ideas will emerge on how to improve the model [Jørgensen, 1988]. Again and again new data, knowledge and experience will drive the development of better models, and this implies that the entire process of model construction is repeated. However, limited resources will inevitably stop the iteration and the modeller will declare the model to be good enough for solving the given problem within the given limitations. For the successful completion of this process, many decisions and choices have to be made, of which only a few are based on purely objective grounds. For the definition of the problem and the definition of the concepts to be used for creating a model, one has to rely on experience, craftsmanship and insight as much as on sound theories of model building which stem from systems analysis and scientific methods.

2.3.2 Categories of models Several characteristics can be used to classify models. The classification can be based on the temporal characteristics of the model, the spatial characteristics and the complexity of the description of the processes. Each of these categories is described.

The temporal characteristics and time dimension of the model When dealing with environmental process models, the models can be classified regarding the manipulation of the time parameter of the model. The first approach is a steady state approach, in which the time parameter is not explicitly dealt with in the model. Steady state models (stationary models, static models) describe the state of the system as an equilibrium resulting from a long period of constant input. The steady state models do not simulate the transient behaviour of the system for the time interval it is unstable, but these models give a description of the stable equilibrium of the system, which may be reached after a very long time span. A general formula to describe this type of models is S=f(I,P)

(2.1)

in which S I P

= state of the system = inputs or forcing functions = parameters

Transient or dynamic models describe the reaction of the system to dynamic inputs. They do describe the transient state of the system, even if it is not an equilibrium state, and they do describe the behaviour of the system during the time span needed to reach equilibrium. Time is one of the important variables in the model algorithms, and the results can be interpreted as the state of the system at a certain point in time. In general, transient models can be described with St

= f(It ,Pt ,t)

(2.2)

in which I and P may change as a function of time t. The spatial characteristics and spatial dimensions of the model The spatial distribution of model calculations, variables and parameters, inputs and results is characterised with the spatial dimensions of the model. A zero dimensional model does not explicitly describe the spatial variability of the different parameters. These models are called lumped models and can be described with:

and

S St

= f(I,P) = f(It ,Pt ,t)

for static models for dynamic models

(2.3)

One dimension spatial models (1D-models) are used to simulate processes along one spatial axis. These are line models, which can be used for example to represent pipes and rivers. Water flow and transport along a line is a spatial distributed process: it can be described as a function of distance along a line. Differential equations can be written to describe the motion of water and constituents along a line. The general formulae for this type of models are:

and

Sx Sx,t

= f(I x,P x) = f(I x,t ,Px,t ,t)

for static models for dynamic models

(2.4)

in which I and P may also change as a function of distance. Two dimensional spatial models (2D models) are used to simulate processes in a plane. These models can be used for example to represent diffusion and flow processes. Water flow and transport over a surface can be described as a two dimensional spatial distributed process, it can be described as a function of position in the

plane. Differential equations can be written to describe the motion of water and constituents over the plane. The general formulas for this type of models are:

and

Sx,y Sx,y,t

= f(I x,y ,Px,y ) = f(I x,y,t ,Px,y,t ,t)

for static models for dynamic models

(2.5)

in which I and P may also change as a function of position. For flow and diffusion processes such as groundwater flow or atmospheric transports 2D models may be inappropriate. The model description should implement a third dimension, and the general process descriptions are:

and

Sx,y,z Sx,y,z,t

= f(I x,y,z,Px,y,z) = f(I x,y,z,t ,Px,y,z,t ,t)

for static models for dynamic models

(2.6)

in which I and P may also change as a function of position (x,y,z). For some processes, the approach in which spatial variability is an integral part of the model is clearly an advantage over models in which this is not the case. However, some processes do not vary as a function of position, and so it is excessive to use a distributed model for these processes. Several 3D processes can be modelled as a stack of 2D layers. Groundwater models can be constructed using different layers for aquifers and confining layers. These models are not genuine 3D models, but since they bridge the gap between 2D and 3D models they are sometimes called 2.5D models.

The complexity of the model The model complexity is determined by the number of subsystems, the amount of state variables and the mathematical equations of the processes in the model. For this discussion we recognize three main classes of (distributed) environmental models, namely • simple (conceptually based) response function models; • conceptually based process models; and • complex physically based models. The group of (conceptually based) response function models does not try to describe the physical processes in the landscape exactly, but the landscape is described as a grey box, with some parameters controlling the reaction of this box. The parameters do not have to have any other than a statistical correlation with the desired output. The parameters used in the conceptually based process models are mostly parameters of which significance for the process is assumed, but the process is not described as detailed as in the physical models. Parameters in the conceptually based process models include slope length, catchment area, average slope, distance to stream and so on. These parameters bear a significant relation with hydrologic processes such as runoff and erosion, and are even of significance for detailed processes such as infiltration and overland flow. Conceptually based model parameter models are using one or more of these parameters to estimate the behaviour of the hydrologic processes under different conditions. Physically based distributed models [Beven, 1985; Anderson and Rogers, 1987] emphasize detailed mathematical representation of the physical processes. These models describe relations between potential fields (such as groundwater potential), resistance or conductivity parameters (such as kD-values) and the resulting fluxes. The governing functions describing system behaviour are based on physical laws such as D'Arcys law. These models use a finite element or finite difference scheme to solve the sets of spatial differential equations that describe the processes.

2.3.3 Choice of models It is difficult to determine the optimum level of complexity (optimum number of subsystems and state variables and the level of process description) for an acceptable level of accuracy. It has been argued that a more complex model should be able to account more accurately for the complexity of the real system; but this not very often true [Jørgensen, 1988]. As increasing numbers of parameters are added to the model there will be an increase in uncertainty. The parameters have to be estimated either by observation in the field, by laboratory experiments or by calibrations, which again are based on field measurements. Parameter estimations are never error free. As these errors are carried through into the model they will contribute to the uncertainty of the results from the model [Heuvelink, 1993]. Distributed parameter physical models have been designed to represent the processes in a theoretically sound manner. They are based on the solution of equations that represent the physical processes that govern the dynamic behaviour of the landscape. Although in theory the physically based distributed models are superior to the other two classes of models their use is not without considerable problems. The results of physically based models may often be in error, despite their 'physical basis'. A major problem for the physical based parameter models is the degree with which reliable location-specific estimates of the values for the parameters can be made. A conductivity parameter estimated for an auger hole may not represent an effective value for the conductivity of a grid-cell of 500 by 500 metres [Bierkens, 1994; Beven, 1989]. The importance of this problem, called the 'parameter crisis' increases as models increase in detail and they need more and better data to drive them [Burrough, 1989]. Analysing the case of the physical based distributed models in greater detail, it can be noticed that most physically based models rely on a number of assumptions that make their use at least doubtful. Several authors [Klemes, 1986a; Beven, 1989; Beven and Binley, 1992; Moore and Hutchinson, 1991; Grayson et al., 1992; Grayson et al, 1993; De Roo, 1993] have recognised the following problems associated with the use of these models: • neither the definition nor the calibration of distributed hydrological models are well established; • it is not clear that the point based equations adequately describe three dimensional, spatially heterogeneous and time varying processes in the real landscapes; • the model structure can significantly influence parameter values; • in theory physical based parameter models should be transferable from one case to another, and by using the appropriate set of parameter and variable values should yield accurate results, but the extensive use of calibration procedures makes this claim at least disputable; and • the ability to validate the model is dependent on the errors in both inputs and outputs, and requires a different set of techniques and data than is traditionally available. Besides these theoretical drawbacks, the application of physical based distributed models, which are developed for small research plots, may be completely unsuitable for decision support that is needed in areas several orders of magnitudes larger. The sheer complexity of the physically based models and the enormous demand for data are arguments for choosing a simpler conceptual model, or even very simple correlation relations. Several advantages of simpler models may be listed. They can be conceptually robust but need not go into too many details, they can use readily available data from GIS and they are quick and cheap to run. Disadvantages may be (amongst others) that there is the danger of oversimplification and a loss of fine spatial and temporal resolution. Denning [1990] argues that 'simplifying assumptions can introduce rather than resolve computational complexities, a possibility that looms larger for systems with many variables and for models with many simplifications'. Many of the more traditional conceptual models are well suited to large areas, but are clearly not capable of providing distributed information [Grayson et al., 1993]. However, simpler models will give the user the opportunity to detect first where and if problems will occur. Based on these results a decision can be made to set up and run a more complex model. Four principles should guide model development [Hillel, 1986]: • parsimony, a model should not be any more complex than it needs to be and should include only the smallest number of parameters whose values must be obtained from data; • modesty, a model should not pretend to do too much, there is no such thing as THE model; • accuracy, we need not have our model describe a phenomenon much more accurately than our ability to measure it; and

•

testability, a model must be testable and we need to know if it is valid or not and what are the limits of its validity.

Increased complexity of a model only yields improved simulation up to a certain level. Given a certain amount of data, the addition of new state variables or parameters beyond a certain model complexity does not add to our ability to model the system, it only adds unaccounted uncertainty [Jørgensen, 1988]. Well-known laws of diminishing returns also apply to model development: 20% of the development time of the model is needed to reach 80% of the results, and an additional 80% of the development time improves the result by only 20% (see figure 2.1).

Figure 2.1 The relation between model complexity, spatial and temporal resolution, knowledge gained and costs of the model. The above yields the conclusion that, although we are very much in search of the PERFECT model, in different cases we need to apply different concepts and different models. It should be realised that choices that have to be made for one of the characteristics of the model highly influence and are highly dependent on choices concerning the other characteristics of the model. In a good model design, there should be an equilibrium between the complexity introduced by the time dimension of the model and the complexity due to the spatial dimension and the process description. The use of a fully dynamic model with small time steps (minutes or hours) for the simulation of the runoff for a large catchment may prove an enormous waste of resources if the catchment is described with one set of lumped parameters. This yields to a set of relations between spatial distribution, temporal resolution and model complexity as shown in figure 2.1. Model designs that are located around the diagonals of these figures are well balanced, models located off the diagonals may suffer from a too detailed description of one or more of the characteristics and at the same time neglecting other characteristics. The validation of the model is the process of evaluating the validity of the model concepts: that is evaluating how accurately the model describes real world processes and which processes are not accounted for. Validation involves the process of evaluating the significance for the original problem of the processes modelled and the

significance of the processes not modelled. Validation of the model is the process of evaluating whether the choices made while defining the spatial scale, temporal scale and process descriptions are sufficiently robust to analyse the processes that are considered relevant for the problem. Models may be validated if they do not violate rules and physical laws, or if there is enough theoretical background to support the concepts. Validation can be based on literature or on experiment. Once again, it is important to realize that there is no perfect model, and any model is only a simplification of reality. The question to be answered in the validation step is not whether the model can be improved (any model can be improved), but whether the increase in costs for improving (in terms of data, time, money and complexity) is balanced by an increase in benefits (accuracy and applicability).

2.4

Integration of environmental models and GIS

2.4.1 Different levels of integration Several authors recognize different levels of integration of GIS and models [Raper and Livingstone, 1993; Fedra, 1993a; Nyerges, 1993; Van Deursen and Kwadijk, 1990, 1993]. The simplest approach is the use of separate GIS and models, and exchange files. This approach requires at least five steps: • input of geographic distributed data through GIS; • export of GIS-data and conversion into the variables and parameters used in the model; • running the model; • importing the results of the model into GIS; and • analysis of the model-results and creating final maps and graphs. Although this approach has the advantage of being straighforward and easy and cheap to develop, its use is not without serious disadvantages. Especially when running several models for a certain analysis, or using different sets of input maps when analysing different scenarios, this ad hoc approach is cumbersome, not very flexible and possibly error prone if it involves a significant amount of manual tasks. An important extension for a fruitful marriage between GIS and models would be the establishment of a common database structure that supports both GIS operations and model runs. In the case of dynamic modelling, this database should not only support the spatial distribution of geographic data, but in addition the storage of temporal (and spatial) distributed input- and control-parameters. With such a database structure, the use of a specific dynamic model can be invoked with one single command, and can be as simple (or complex) as the use of any other GIS-command. Any integration at this level, however, requires a sufficient open GIS architecture that provides the interface and linkages necessary for tighter coupling [Fedra, 1993a]. This deeper level of integration would merge two approaches. The model becomes one of the analytical functions of the GIS, or the GIS becomes yet another option to generate, manipulate and display parameters, input and results of the model. Because there are so many models it is difficult to choose which models should be incorporated into this medium level integrated GIS - dynamic model environment. One could choose well-known models for different fields of interest, such as SHE [Abbott et al., 1986], TOPMODEL [Beven, 1985], MODFLOW [McDonald and Harbaugh, 1988] and ANSWERS [Beasley, 1977; De Roo, 1993] for hydrologic purposes, but a useful general purpose alternative would be to extend the GIS with a (limited) set of general tools that can be used to extract relevant parameters and build environmental models to meet the user's requirements. This is an extension of the approach used by Tomlin [1983] when he designed the Map Analysis Package. Instead of implementing a limited number of specific solutions for geographic problems, the GIS is a toolbox, with which an experienced user can build solutions to solve many spatial problems. This high level approach yields a powerful tool for storing, retrieving and analysing geographic data and allows one to explore how the processes of landscapes may react to human interference.

Figure 2.2

Levels of integration between GIS and (dynamic) models.

Although the distinction between the different levels of integration (figure 2.2) is vague, the levels can be ranked as: Level 1 Low level

Standard GIS -> Manual exchange of files -> External model : :

Level 2 Medium Standard GIS -> Automated exchange of files -> External model : : Level 3 High level Integrated GIS with modules for generic modelling The low level linkage is characterised by the use of conversion programs and procedures, and data exchange between models and GIS using (in most cases ASCII) files. The medium level of linkage is characterised by an automated and transparent procedure for exchanging data, mainly through the use of a common database, and allowing the model to address this database directly. In the high level of integration, the distinction between model and GIS becomes vague, and a dynamic model becomes just one of the applications that can be constructed using the generic functionality of the GIS toolbox.

Low level integration

Medium level integration

High level integration

Figure 2.3

advantages

•

the development of a low level integration is less time consuming than the development of higher level integration • use of existing programs for GIS and dynamic models yields well known and reliable components for spatial modelling disadvantages • labourious and time consuming • not flexible • error prone because several steps of user interaction are required • new versions of GIS or model require modification of conversion software • redundancy and consistency problems due to the use of several instances of the same database advantages • entire GIS functionality available for manipulation and analysis of input and results of the model • increased speed (no overhead for conversion of data) • easier maintenance of databases, reduced redundancy and consistency problems disadvantages • requires a relatively open GIS structure • low level approach for model formulation advantages • integration of GIS functionality for manipulation of input, results and formulation of the models • no overhead for conversion between GIS and models and between individual models • rapid development of new models • easy maintenance of models disadvantages • current generation of commercial GIS does not fully support dynamic modelling • investment in development of tools and functionality is high • lack of specialists insight may yield invalid model concepts and formulations, the user is fully responsible for the model formulation The advantages and disadvantages of the levels of integrating GIS and dynamic models

2.4.2 Current status of the link between GIS and dynamic models A large number of applications have been developed recently, which link GIS to some form of environmental modelling. To a large degree, these applications can be classified as applications having a low level of integration between model and GIS. Examples include the linkage between MODFLOW and the ARCINFO package (eg. Hoogendoorn [1993]), MODFLOW and GENAMAP (eg. Kamps et al. [1993]) or ILWIS and MICROFEM [Biesheuvel and Hemker, 1993]. This approach yields very useful results, because ARCINFO, GENAMAP, ILWIS, MICROFEM and MODFLOW are all well known and very reliable programs. As already mentioned the approach requires at least five steps in which data has to be reformatted, for which a large number of tools is now becoming available. The advantage of the approach is it's operational status, but whenever a new model is developed which should be linked to the spatial database, the whole procedure of writing reformatters should be repeated. In practice, the use of low level linkage yields a number of difficulties. The primary use of the GIS databases might be completely different from the required use in the model. The databases are poorly geared to be used in the models, and the results of the model are difficult to be incorporated in the structure of the GIS database. It is therefore that the linkage between GIS and the model is an ad hoc solution. Frequently the linkage between the

model and GIS is an once-only exercise, and the database used for the model is not updated along with the GIS database. The medium level integration between the model and GIS is realized in approaches where the database of the model is adapted so that it can be mapped directly on the GIS database. The required more open GIS database structure is not available in the above mentioned GIS systems, but several examples can be found in literature in which GRASS is linked to hydrological models such as ANSWERS (eg. Rewerts and Engel [1991]) and TOPMODEL (eg. Chairat and Delleur [1993], Romanowicz et al. [1993]). The authors of the latter paper define their implementation of TOPMODEL as a Water Information System (WIS), and remark that it can be considered one of several hydrologic application modules to become available in GRASS. They point out that there is a very important aspect of the integration of GIS and distributed models that must be emphasized. TOPMODEL has never been considered as a fixed model structure but rather as a set of modelling concepts that can be adapted and modified by the user. Thus, the general implementation of TOPMODEL allows for a userinteractive flexible adjustment of model structure depending on both predicted patterns of behaviour and the aims of the study.

The authors recognise three ways of integrating such a user-definition of model structure within GIS: • provide a set of variant structures as compiled routines that may be selected from a menu; • allow the user to provide an executable program segment with standardized inputs and outputs; or • provide a meta-language within which the user may define and modify the model structure. Their WIS provides the capability to define models using the first two mentioned methods, and thus provide for a possibility to create a user defined model choosing from a number of predefined possibilities. The same approach is followed for the design of the Modular Modelling System MMS [Leavesly et al., 1993]. They argue that the increasing complexity and interdisciplinary nature of environmental problems require the use of modelling approaches from a broad range of science disciplines. They describe their approach as to selectively couple the most appropriate process algorithms to create an 'optimal' model for the desired application. In addition, their system allows for the coupling of a variety of GIS tools to characterize the topographic, hydrologic and biologic features of the watershed for use in a variety of lumped or distributed parameter modelling approaches. This latter feature of the MSS represents another important field of linkage between GIS and environmental models: the MSS is using the GIS data set to derive model parameters that can be used in external models. For most environmental modelling projects, GIS is seen as a convenient and well-structured database for handling the large quantities of spatial data needed. Traditional GIS tools such as overlay and buffer are also important for developing derivative data sets that serve as proxies for unavailable variables [Kemp, 1993a; Fedra, 1993c; Gao et al., 1993; Moore et al., 1993; Maidment, 1993a]. Topographic features such as watersheds, ordered stream networks and topographic surface descriptors such as flow accumulation and flow length can be computed from an input DEM using functions available in current GIS. These features and surface descriptions are of primary importance for most surface hydrology models. A somewhat different approach is advocated by Fedra [1993a]. He considers the problem of linking dynamic models and GIS as a part of the task of building spatial Decision Support Systems (DSS). Any efficient DSS should allow a user to select criteria, and arbitrarily decide whether he wants to maximize or minimize them or use them as a threshold for eliminating alternatives. However, the most important part of the DSS is the generation or design of the alternatives: if the set of alternatives to choose from is too small, and does not contain satisfactory (or 'optimal') solutions, the best ranking and selection methods cannot lead to satisfactory results. A decision support system for spatial problems requires the capability to manipulate, display and analyse spatial data and models. Alternatives need to be generated efficiently, analysed and compared. By excluding certain basic GIS functions, such as data capture (ie. digitizing), and concentrating on the display and analysis of sets of thematic maps and model output, GIS functionality can be embedded into a DSS framework. Most of the analytical functionality is performed at the level of the model. Fedra argues that the distinction between model and GIS becomes blurred, and meaningless if the model operates in terms of map overlays, and the analysis of map overlays is done by the model. The previous sections described several characteristics of the levels of integration. Figure 2.3 summarises the advantages and disadvantages of the recognised levels.

2.4.3 Required GIS functionality for high level linking with dynamic models As can be concluded from the above, the high level integration is superior for a flexible formulation and implementation of a large number of dynamic models. However, the high level integration of GIS and dynamic environmental modelling is hampered by a lack of some essential parts in the functionality of the GIS. While dynamic environmental models deal with dynamically changing continuous data, current GIS manage only static data. The current generation of GIS is not very well geared to implement these descriptions. Although some GIS are capable of managing continuous data, the emphasis in most current GIS is on discrete objects. Since environmental models generally depend upon physical principles, the mathematics of these models is often in the form of differential equations that describe motion, diffusion, dispersion, transformation or some other meaningful properties of continuous phenomena [Goodchild, 1993; Kemp, 1993b]. Although the current generation GIS may be used to construct 1D process models, which are mostly vertical movement models, they lack functionality for the 2D and 3D description of lateral processes such as diffusion and dispersion processes (figure 2.4). The GIS should include all necessary primitives to allow for expression of these continuous phenomena. The level at which the individual primitives are defined should be closely related to the discipline of environmental modelling, without sacrifying flexibility to create models from scratch.

Figure 2.4

Flows and state in a spatial dynamic system.

The data model used should be based on a functional distinction between continuous and discrete entities. The system should eliminate the necessity to consider the implementation of the discretisation whenever possible. Moreover, for a high level integration of GIS and dynamic models, the systems should integrate support for dynamic variables, and allow for the use of time series describing changes in these variables over time. The next chapters describe a prototype GIS that incorporates a large part of this preferred functionality.

3

MODELS AS AN INTEGRAL PART OF GIS It does not seem to be productive to try to accomplish such simulations by intrinsic GIS functions; rather the simulation model should be kept separate from the GIS and just use the GIS as a spatial data source. (Maidment, 1993)

3.1

Introduction

This chapter deals with the high level integration of models in GIS. First the approach of using GIS script languages derived from Map Algebra and Cartographic Modelling techniques is discussed. It is argued that Map Algebra can be considered as a normal (although very specialised) computer language. The deficiencies of Map Algebra and Cartographic Modelling related to dynamic modelling are discussed. Before describing the criteria for the development of a GIS script language that overcomes these disadvantages, this chapter discusses some general aspects of dynamic models for environmental problems, and some aspects of computer languages and data structures.

3.2

Map Algebra and concepts of implementing models in GIS

Map Algebra is a structured integrated set of primitives that can be used to create spatial models. Although there are several versions of Map Algebra, all with different names, most of them seem to stem from one system, the MAP (Map Analysis Package) designed by Dana Tomlin [Tomlin, 1980]. Map Algebra consists of a set of primitive operators for map analysis, which can be linked into script files to perform complex analysis. As such, it is a computer language, which can be used to instruct the computer about the sequence of operations necessary to perform a certain operation. The linking of these Map Algebra commands into scripts used to instruct the computer how to obtain a certain result is usually referred to as Cartographic Modelling. Tomlin describes Cartographic Modelling as an approach that '... attempts to generalize and to standardize the use of geographic information systems. It does so by decomposing the data processing tasks into elementary components, components that can then be recombined with ease and flexibility' [Tomlin, 1990]. The concept of combining the Map Algebra commands to form a Cartographic Model script is similar to the combining of the keywords of a computer language to create a program. The commands available in the Map Algebra are the primitives of the operations that are possible with the language. Operations in the Cartographic Model are either available as keywords in the Map Algebra language or can be easily constructed using the language. The major goal of the Cartographic Model script (and similar for computer programs) is to structure the problem in smaller steps and to instruct the computer in an unambiguous way what (GIS) commands should be performed to reach a certain result. Several examples of the use of Cartographic Modelling are given by Burrough [1986] and Tomlin [1980, 1983, 1990]. As has been observed above Cartographic Modelling languages can be considered as regular computer languages. The property that distinguishes Map Algebra from other computer languages is the fact that it is not a general purpose computer language, but one especially designed for spatial analysis. This means that many operations available in general purpose computer languages are not available in the Map Algebra languages, while commands that would take an enormous amount of coding in general purpose computer languages are available through one or only a few commands in the special purpose language. In general, good computer languages will [Highman, 1967]: • allow you, somehow or other, to do anything you want to do which can be defined in the context of your problem without reference to machine matters which lie outside this context; • make it easy to express the solution to your problem in terms which conform to the best practice in the subject;

• • • • • •

allow such solutions to be expressed as compactly as possible without risking obscurity which often accompanies compactness; be free of any constructs which can give rise to unintentional ambiguities; permit the sort of ambiguity which is resolved dynamically, if the nature of the problem calls for it; take over without change as much as possible of any well-formed descriptive language which is already established in the field in which the problem originates; allow for maintenance and easy apprehension: it should be possible to read and understand your own programs and be able to change them without running too large risks of screwing up and it should be possible to read other people's program and understand how they solve the problem; and allow for structuring the problem and evaluating and assessing the correctness of the approach.

GIS-languages developed for implementing dynamic models should be evaluated using the same set of criteria. Based on these criteria, the efficiency of a computer language can be considered. Efficiency can be measured for a number of aspects: • speed of execution; • space requirements; • efforts required to produce a program or system initially; and • efforts required to maintain the program. Of these criteria, the first two are beyond the field of specialisation of geographers: they are highly linked to software engineering and available hardware. In the early days of computing, both speed of execution and space requirements were of primary importance, and failing on one or both criteria could easily mean the failure of the project. As the power of hardware increases, the importance of these hardware-related criteria decreases. Even if an approach is too slow or too memory and disk space consuming by today's standards, in two years time the performance of hardware will have doubled, and the critiques may very well be outdated. The third and fourth criteria are much less related to hardware and software engineering, and have much more relationship with the geographers and their field of expertise. Ultimately, the final test of the efficiency of modelling languages for dynamic models within GIS is whether geographers, hydrologists and environmentalists can use the language without too much effort to produce and maintain models for their fields of interest. Although quite a number of successful implementations of environmental models using Map Algebra and Cartographic Modelling exist, the strong emphasis of the current versions is on the querying of a static database. From this static database, new data is derived which is added to the database, thus increasing the amount of information in the database. The current versions of Map Algebra and Cartographic Modelling do not explicitly allow for time dependent phenomena to be stored and analysed. As discussed in chapter 2, there is a serious weakness when one tries to apply cartographic modelling techniques for modelling continuous phenomena and dynamic modelling fluxes of energy and substances through the landscape. Kemp [1993] discusses a strategy to deal with these issues. Her list can be considered as a list of requirements for the next generation of Cartographic Modelling languages: • allow expression and manipulation of variables and data about continuous phenomena in common symbolic languages; • provide a syntax for incorporating primitive operations appropriate for environmental modelling with fields, but are not yet available in GIS or common programming languages; • guide and enable the rapid development of a direct linkage between environmental models and any GIS; • the strategy should be capable of being incorporated into computer language implementations of environmental models; • provide structures representing fields and incorporation of the concept of vector fields; and • eliminate the necessity to consider the form of the spatial discretization (the data model) whenever possible. The first points are related to the issue of the level of the language. The last points are related to data structures and data models. These issues are discussed in more detail in section 3.3.

3.3

Development of a dynamic cartographic modelling language

For the design of a computer language that can be used as a toolbox for dynamic modelling in GIS, three aspects are important: • What is the level of abstraction of the language, is the level of abstraction appropriate for the problems that you want to solve? − Are you capable of constructing the operators that are not part of the language from the primitives given in the language, is the minimum number of primitives available sufficient for this field of applications? − Are the primitives generic enough to be used in many problems? − Is it possible to express the solution in terms that have any meaning in the field of practice, do the primitives represent recognisable operations in the field of practice? • What is the data model used? − What is the data structure for the spatial data? − Do the data types represent any recognisable phenomena in the field of practice? − What is the data structure for the temporal data? • What are the control structures the language allows for? − Is there the necessity to create loops and iterations? − What control does the user needs over the sequence of calculations? − What control does the user has over the flow of the program (branching and conditional execution)?

Levels of abstraction; how to approach the problem The first aspect deals with the level of abstraction. Abstraction is the process of identifying the important aspects or properties of the phenomenon being modelled. Using a more abstract level, one can concentrate on the relevant aspects or properties of the phenomenon and ignore the irrelevant ones. What is relevant depends on the purpose for which the abstraction is being designed [Ghezzi et al., 1982]. The level of abstraction determines the amount of commands that are necessary for a certain complex analysis. Increasing the level of abstraction means that one can more specifically address the problem. One needs fewer operators for solving the problem because each operator can perform a more dedicated task. Increasing the level of abstraction results in a more specific set of operators, each having a more specialist purpose. However, to solve many different problems, one needs a larger set of operators to choose from. Increasing the level of abstraction means that the set to choose the operators from is larger, but the number of operators required to perform a complex task decreases. This might result in a very high level language, for which the field of application becomes too narrow, or their command set becomes too large. Using languages with a low level of the abstraction, the programmer or user has to instruct the (GIS) system how to solve the problem. The user is responsible for the description of the structure of the problem and has to code the algorithms necessary to solve the problem. The computer language is a means to define how to solve the problem. Using higher levels of abstraction means that the focus is shifted from the algorithms of solving the problem to the description and structuring of the problem to solve. This can be made clear by looking at the problem of creating buffer zones around major rivers in a digital database. Using low level languages the user has to tell the computer that he wants to create a map containing these buffer zones, and he has to code in a program how the computer should create these buffer zones. With a high level language the user only has to tell the GIS that he wants buffer zones, while the system itself is responsible for the algorithms how to create these buffer zones. The level of the language does not tell much about the capability of the language to perform a certain task. A low level language, such as assembler, a general purpose language such as C and a high level language such as Map Algebra are all capable of implementing the program to find the buffer zones around the major rivers. The implementation of a program to solve this problem would require approximately one to five lines of code in Map Algebra. A general purpose language such as C would need a few hundred lines to implement this problem, while assembler could easily require tens of thousands of lines. Clearly the task is implemented most effectively in the highest level language. However, it is obvious that it is impossible to write a multi-user operating system using Map Algebra.

Data structures and data models; raster or vector, that's not the question The second aspect of the design of a computer language in general and a GIS-language for dynamic modelling is the design of the data model. The architecture of the data management system determines the design of the descriptive constructs used for data storage. As such, it is the fundamental mechanism for determining the nature of data representation as presented to application [Nyerges, 1993]. Computer languages are constructed around data types and data models. The language is the means by which the the data can be analysed and manipulated. Clearly, for Map Algebra and Cartographic Modelling the data type under consideration is spatial data. There are only a few primary data structures for storing spatial data. These have been long recognised and are responsible for the division in the GIS-world between vector and raster approaches. However, the breakdown of data structures into raster and vector is not determined by the aims and purposes of GIS, but is a relic from the times that GIS was limited to a graphic map making environment. As GIS is used more and more for analytical purposes, the subdivision in raster and vector is not only too primitive, it may very well be completely obsolete and superfluous. Eventually, GIS-data will be stored in one form or the other, but for a functional support of the analytical capabilities of GIS, much more effort should go into a more sophisticated design of the data model. A more sophisticated design of the database should be based on the characteristics of the entities of interest. The entities are not related to the computer or the data structures geographic data should be stored in digitally, but relate to the landscape and environment outside the computer. This simple fact means that we are not interested in the way the computer can store entities (the mechanics behind the database), but what we recognise as entities to be stored and manipulated (the concepts of the use of the information). For dynamic modelling, the important entities may include information concerning water, soils, land use and population. These entities can be stored using the well known geographic primitives such as points, lines and polygons, or rasters, but by doing so, we neglect important information about the type of the entities. Adding additional type information allows for a more intelligent use of the database and helps preventing errors and mistakes based on misinterpretation of the data. The mechanism of data storage to use can be classified as raster or vector, but the type of the entity we want to store can hardly be described in terms of raster or vector. If we consider the use of the entities for dynamic modelling purposes, a much more useful typing (although still very primitive) is in terms of continuous (physical) fields and classified objects. Objects are those entities that may be counted, moved around, stacked, rotated, coloured labelled, cut, split, sliced, stuck together, viewed from different angles, shaded, inflated, shrunk, stored and retrieved. Objects are characterized by qualities of discrete identity, relative permanence of structure and attributes and their potential to be manipulated [Couclelis, 1992]. Objects result from human action (building, constructing, allocating) or classification. A physical field is traditionally defined as an entity that is distributed over space and whose properties are functions of space coordinates and, in the case of dynamic fields, of time [Kemp, 1993]. Spatial continuous phenomena are best described by the concept of the field. Two types of fields may be recognised. Scalar fields are characterized by a function of position and, possibly, time, where each point is a scalar, while vector fields are characterized by a vector, i.e. both magnitude and direction. Scalar fields can be used to describe intensities and potentials, such as temperature, population density, precipitation etc. Vector fields are defined if not only magnitude but also direction is known. Vector fields can be used to represent (horizontal) fluxes and forces, such as ground water movement and movement of air (wind and storms). Objects are measured on nominal or ordinal scales (qualitative scales). Objects can, however, contain attributes that come from interval and ratio scales. Fields are described in terms of ratio and interval scales (quantitative scales), and never as nominal and ordinal scales. Objects may be classified fields (such as soil maps where each soil type is an object, or topographic maps with polygons delineating areas (objects) with an elevation between two values from the interval scale of elevation), or artifacts of human interference. Fields may be clustered to construct objects, which may be delineated because they embody a common set of values (soil maps, topographic map). Obviously, more mathematical operations are allowed with a quantitative scale than with a qualitative scale.

From the discussions on data models and data structures [Couclelis, 1992; Kemp, 1993; Goodchild, 1992; Burrough, 1992; Burrough and Frank, 1995], it is clear that the technical question of the most appropriate data structure leads to the philosophical question of the most appropriate conceptualization of the geographic world. This question is stated by Couclelis [1992] as 'Is the geographic world a jig-saw puzzle of polygons, or a club sandwich of data layers?'. This search for the most appropriate conceptualization is closely linked to the question whether the world surrounding us is made out of discrete and independent objects or made out of numerical fields that give rise to purely accidental clustering of some part of the field yielding a set of unstable, fleeting objects. The breakdown in camps in this discussion seems to follow the same delineations as can be recognised in the vector versus raster debate. People who want to conceptualize the world as identifiable objects seem much more happy with the vector environment, while people who want to see the world as fields, or at best as vague, weakly definable objects are defending the raster approach. It should be realised however, that despite the philosophical questions whether 'reality' can be defined as crisp objects or as a spatio-temporal realisation of fields, scientists tend to use the most appropriate concept for the specific question or purpose. The question is not whether the world consists of fields or objects, because quite a number of geographic entities can be viewed both as an object or a field, depending on the application. The major question is whether we want to use a field-based or object-based view for a certain entity for the analysis of a certain problem. This implies that the main reason for storing geographic phenomena in the computer is not to represent the 'geographic reality' as accurate as possible at all cost, but to store geographic phenomena as accurate as possible and required for a certain purpose. It is the purpose why we store a certain geographic entity that should drive the choice between object and field representation. The data model is always a simplification of reality, and the quality of the choice for a specific data model is determined by the phenomenon studied and the specific questions to be answered. There will always be a need for the description of reality as both a crisp object related description as for the field description. The main purpose of the discussion is not to define one data structure that can store all geographic entities and possible views, but to allow for the appropriate data type to be chosen for a specific geographic phenomenon or entity. If we consider the Cartographic Modelling and Map Algebra as defined by Tomlin and Berry [1979], the conclusion can be drawn that Map Algebra is stronger related to the object data models than to the field models. A large number of operators on objects are defined, while the analysis of spatial fields is much weaker developed. Constructing operators using the concepts of vector fields are virtually impossible with the standard Map Algebra. Moreover, Map Algebra is designed to work with time-independent databases: the variables stored in the database do not change as a function of time. Cartographic Modelling can be used for dynamic modelling, but the burden of keeping track of time dependent variables, inputs and result are totally on the shoulder of the user. As discussed, the choice of describing the geographic entities using more meaningful type definitions such as fields or objects (conceptual types) is a much more fundamental one than the question whether the data should be stored as vector or raster (technical implementation structures). This choice defines the measurement scale of the entity stored, and thus the choice between a field representation and an object representation defines very clearly which operations are permitted on the entity. This has much more important implications than the question whether these operations are implemented in the specific data structure. In both vector and raster systems, we can implement operations for counting, adding, combination and finding the shortest route between hospitals and accidents. However, operations such as the addition two overlays that contain soil types (= objects with a nominal scale) will yield unwanted results, no matter whether implemented in a raster or vector domain. In general, we can see that implications of the choice between the qualitative scales (nominal and ordinal scales) and the quantitative scales (ratio and interval scales) is a very important one. Although technically very achievable, entities on a nominal scale do not support any mathematical operations, whereas fields allow for an extensive set of mathematical operations. It is not the (technical) data structure that determines if the operation is permitted, but the data type that is responsible for the set of operations.

Strong type checking versus loose type checking There is always the discussion on how strictly to apply data typing. One standpoint in the discussion is that strict data typing is a restriction on the possible combinations of operators that a user may want to perform. The argument is that the user may have a very specific question in which he wants to perform an operation on a type

that would in theory not allow such an operation. Examples are that there might be a complex analysis in which it may be useful to take the square root of the entities that are in a soil map. The soil map may be stored as a large number of positive integer values, each representing one category in the soil map. Taking a square root from these positive integer values is a completely valid operation and the language should not prohibit this kind of analysis. The opposite attitude is that operations never yield valid results if the data used for the operation is not appropriate for this operation. There may be a single analysis in which a square root of a soil type yields a result that can be interpreted, but in general this operation is nonsense. Therefore, these mathematical functions should not work on the soil type map. If the necessity exists for an operation to be performed on an inappropriate data type, it simply means that the set of commands is not complete, and a complementary command should be defined, capable of performing the wanted operation in the proper type domain. Adding strong type information to data also allows for the implementation of polymorphic functions. A certain function or operation may have different functionality based on different types of input. This can be explained by analysing resampling and interpolation operators. If no data type information is supplied, the user has to decide which method of interpolation and resampling should be used, and most GIS offer the choice between a nearest neighbour and a (bi-)linear interpolation. However, if the data supplied to the operator is classified data, the option of using a (bi-)linear interpolation would not yield any useful results, while if the data supplied is from a continuous scale, the bi-linear interpolation would yield highly superior results over the nearest neighbour approach. Although most GIS provide the user in this case with an option to choose, if the type of the data is known, the operation can determine the optimal approach without consulting the user. As a result of a sound typing and type checking mechanism, more intelligence can be added to the system. Although the discussion is an ongoing one, it has long been recognised that there is some substantial motivation for strong data typing. Summarising, the following list can be given: • types help to understand and organise our ideas about entities; • a type scheme helps to see and discuss unique properties of specific types; • types help to detect errors; and • types allow for polymorphic behaviour of functions and operators. The division of data in field (or continuous) data and object (or classified) data is hardly sufficient for all purposes. We should be careful to expect the fact that we add type information to geographical data will prevent all errors. The fact that an operation is permitted on a certain set of geographic information does not guarantee the meaning and sense of the operation. However, adding type information allows for mechanisms to avoid those operations that will absolutely make no sense. The classification in fields and objects can be considered as the primitives of a more functional typology of geographic information. The field versus object classification of geographic data may prove to be a much more stable root to support a more intelligent and robust tree of data structures than the vector versus raster classification.

Control structures in computer languages Most of the conventional computer languages offer a set of constructs for creating loops and explicit construction of iterative procedures. Loops are those constructs that allow for repeatedly execution of a (set of) statements. Although most conventional computer languages allow for loops, several languages may be listed that do not include these constructs. Within the framework of dynamic spatial modelling, these constructs are useful to a limited set of purposes: • iteration over space; • iteration over time; and • iteration to increase accuracy of the calculations. The explicit iteration over space is essential if the entity addressed by the operators is only part of the total spatial coverage of the database layer. Operators that address individual cells in raster maps need to be executed repeatedly to be applied to the total database layer. Operators that address entire maps do not have to be executed iteratively, although their internal implementation might include several loops.

If the operator addresses individual cells in the raster database layer, the instruction of multiplying cell values by 100 (to yield values in centimetres instead of metres) could be implemented with /* operator addresses individual cells */ for (row = 0; row TempThres) then LengthOfGrowingPeriod+1 else 0); MaxLengthOfGrowingPeriod = max(MaxLengthOfGrowingPeriod,LengthOfGrowingPeriod); # The storages and transports of the dynamic system storage SoilWaterStorage: initial SoilWaterStorage = InitSoilWater; transport Infiltration to SoilWaterStorage: Infiltration = f( Precipitation,SoilWaterStorage....); transport ETact from SoilWaterStorage: ETact = f ( SoilWaterShortage,ETpot, ...); transport Percolation from SoilWaterStorage: Percolation = f( SoilWaterStorage,.....); transport UpwardSeepage to SoilWaterStorage: UpwardSeepage = f(....,SoilWaterStorage,....);

5.3

Accumulation of water in catchments

This section describes techniques used for simple overland flow and accumulation of water and materials over a topological network. The techniques described in this section are called steady flow techniques. These are not fully dynamic modelling techniques as they do not allow for a description of the processes occurring during the flow over the topological network. For dynamic approaches for overland flow routing and accumulation see section 5.5. It is assumed in this chapter that the amount of water or material to be transported over the network is known, and not part of the description of the accumulation process.

Simple accumulation of excess precipitation, surface water or other material over the LDD map introduced in chapter 4 is done with the function accu and associated functions. The use of the accu-functions in iterative modelling assumes that all available water will discharge through the outlet within the same time step it becomes available. This steady flow approach is reasonable if the time step is long compared to the time of travel of water through the channel network, and no information is needed on the timing of runoff events within the time step. If the time step becomes smaller and approaches the order of magnitude of the travel time through the network, the use of the accu-functions becomes less recommended. It is clear that now the assumption that all water discharges within the same time step becomes questionable, and the more advanced routing routines of section 5.5 should be used. The function accuflux operates on the LDD map to yield a map with on each grid cell the amount of water or material that traversed this cell on its way to the outlet. The accompanying function accustate yields a map containing the state of the system after accumulation of water. For each cell this map contains the amount of water that is not transported but left behind in the cell. As a consequence of the functionality of accu, accustate yields a map in which all water is accumulated in the pits of the catchment, since accu does not allow for any water to stay behind during the lateral transport process. All cells not denoted as a pit or outlet thus contain a value of zero. The function accustate has been added for consistency with the other accu related functions. The accustate and accuflux functions do allow for additional water to be added to the transport network (lateral inflow into the channel), but they do not allow for any subtraction of water from the channel during the transport process. This implies that processes such as infiltration of upstream water in the river bed or evaporation from the river surface cannot be accounted for. If these processes become more important, the functions accuLTC, accuTT and accufraction are more appropriate. The application of these functions is discussed later in this section. Accuflux can be used for accumulation of all kinds of materials, as long as the above mentioned assumptions are accepted as valid. Given the input of surface water (in the map SurfaceWater) to be accumulated through the topological network (in the map LddMap) the function call is StreamFlux = accuflux(LddMap,SurfaceWater);

I now introduce an example catchment with a topological network as given in figure 5.3a. Assuming a constant of 1 mm for SurfaceWater, the result of the accuflux function is given in figure 5.3b. Given a constant input of a highly soluble pollutant that will not react or deposit on the bottom of the stream, the concentration of the pollutant in the stream can be determined by dividing the amount of pollutant transported through the system by the amount of water flowing through the stream network. This yields the following script file fragment StreamFlux = accuflux(LddMap, SurfaceWater); PollutantFlux = accuflux(LddMap,Pollutant); Concentration = PollutantFlux / StreamFlux;

Applying this script file to the results of the example catchment, and introducing a point source of this pollutant (figure 5.3c) yields a concentration map as given in figure 5.3d. Applying the script file to the situation in which non-point sources of the pollutant are distributed through the area as in figure 5.3e yields a stream concentration as given in figure 5.3f. Although useful as a first indication, attention should be paid to the fact that the assumptions underlying the accu functions are very restrictive and real world situations will not meet these assumptions most of the time. An improvement of the above is the introduction of losses during the transport process. As explained in chapter 4, the process of transport and losses may be described as the result of four different mechanisms: • transport of the surplus occurs after a certain threshold of losses has been reached (function accuTT); • losses occur because transport capacity is limited (function accuLTC); • losses occur as a fraction of the material from upstream (function accufraction); and • massive transport of all the supplied material occurs once a certain threshold value has been exceeded (function accutrigger). Although these mechanisms are orthogonal, which means non of the mechanisms can be written as a function of the others, their use and results are similar. In this section, several applications of the use of these functions are given.

Figure 5.3

a Local Drain Direction map for example area b Result of accuflux with uniform input c Point source pollutant d Concentration of pollutant in stream network e Diffuse source pollutant f Concentration of pollutant in stream network

Figure 5.4

Transport of surplus after a threshold of losses has been reached (function accuTT)

The first process discussed is the transport of the surplus of material once certain losses have been met. This may be the case with influent streams, river streams in a dry climate, flowing on plains underlain by sand and gravel, with a relatively deep ground water table. The influent stream will lose water by seepage through the channel floor. This water recharges the ground water body. If the infiltration rate in a channel cell is assumed to be constant, upstream water must meet this infiltration demand first and only the remainder can flow to the next cell. The concept is characterised by the fact that losses are limited, and not dependant on surface water flow. If sufficient water is supplied, the demand for infiltration will be met and the surplus is allowed to flow through. If insufficient water is supplied, the demand is met as far as possible, and no surplus water will flow through (see figure 5.4). Assuming that the infiltration rate through the channel flow is known and available in the map KnownInfiltrationRate, and the amount of excess precipitation available for runoff is given in the map ExcessPrecipitation, the accumulation of water through the catchment can be modelled with StreamFlux,Losses = accuTTflux,accuTTstate(LddMap,ExcessPrecipitation,KnownInfiltration)

For each grid cell the resultant StreamFlux map will contain the amount of water passed through to the next cell, while the Losses map contains the actual infiltration in each cell. The example can be extended by taking the capacity of water for sediment transport into account. This transport capacity depends on flow velocity, and thus directly related to flow volume. The example does not deal with the mechanisms underlying the erosion sedimentation process; the reader is referred to studies devoted to these processes [de Roo, 1993; de Jong, 1994]. Without paying attention to the underlying mechanisms, the relation between transport capacity and flow volume may be written as: TransportCapacity = f( StreamFlux, .... )

(5.10)

Detached soil particles will be transported only if the transport capacity of water is sufficient, and once the supply of detached soil particles and the transport capacity of the stream network are known, the function accuLTC can be used to determine the pattern of transport and sedimentation. The function to determine sedimentflux and sedimentation becomes SedimentFlux,SedimentLoss = accuLTCflux,accuLTCstate(LddMap, Sediment,TransportCapacity)

The total script file now becomes # Simple erosion/sedimentation modelling # Author: WPA van Deursen # Date: january 20, 1995 dynamic SurfaceWater = ....; Sediment = ....; StreamFlux = accuflux(LddMap,SurfaceWater); TransportCapacity = f(StreamFlux,...); SedimentFlux,SedimentLoss = accuLTCflux,accuLTCstate(LddMap, Sediment,TransportCapacity);

5.4

Using GIS for the determination of the Unit Hydrograph

The techniques described in the previous section do not allow for an analysis of the timing of accumulation and runoff events. For this analysis, detailed consideration must be paid to the process of lateral flow and overland flow. This and the next section describe techniques for analysing the timing of the runoff process. This section describes the implementation of a technique called the Unit Hydrograph, which is essentially a description of the unit pulse response of a linear hydrologic system. Although the Unit Hydrograph method yields a time series of runoff occurring as a result of (several subsequent) precipitation events, it cannot be considered a component of a spatially distributed dynamic model. The Unit Hydrograph application as described here does not yield a distributed analysis of the resultant hydrographs, and the assumptions on which the Unit Hydrograph theory is based are too restricted to be used in such type of models. In particular, the use of the Unit Hydrograph assumes that the local flow velocities of surface water are known in advance and invariant through time. These shortcomings and assumptions make the application of the Unit Hydrograph in dynamic modelling troublesome. Section 5.5 describes the routing routines that are less restrictive and can be implemented in dynamic models. However, the Unit Hydrograph presents a simple and direct method for analysis of rainfall-runoff relations for catchments. The concept of the Unit Hydrograph, introduced by Sherman in 1932, is considered a major step in the analysis of rainfall runoff relations for catchments. The Unit Hydrograph is defined as the surface runoff hydrograph resulting from effective rainfall falling in a unit of time (such as one hour or one day) and produced uniformly in space and time over the total catchment area [Sherman, 1942]. The Unit Hydrograph method makes several assumptions that give it the simple properties assisting in its application. These assumptions are: • there is a directly proportional relationship between effective rainfall and surface runoff (proportionality); • the surface runoff hydrograph of a number of successive amounts of rainfall can be obtained by the summation of the component hydrographs due to the individual storms, each being lagged by the appropriate time (superposition); and • the Unit Hydrograph concepts assume that the effective rainfall - runoff relationship does not change with time (the assumption of invariance). The above assumptions cannot be perfectly satisfied under natural conditions. They imply unchanging characteristics of the catchment and an excess rainfall hyetograph that is uniformly distributed throughout the area. Both implications of the concept have limited validity. Effective rainfall may be very dependent on the state of the catchment before the storm event, and subsequent rain storms may produce incomparable surface runoff hydrographs. The assumption of uniform distribution of rainfall is very rarely met. For small or medium sized catchments, a significant rainfall event may extend over the whole area, but more usually, storms vary in intensity in space and time and runoff response is often affected by storm movement over the catchment. However, when the hydrologic data to be used are selected carefully so they come close to meeting the above assumptions, the results obtained by applying the Unit Hydrograph are generally acceptable for practical purposes. The Unit Hydrograph method has the advantage of great simplicity. Several approaches exist for the derivation of the Unit Hydrograph. They are based either on statistical analysis of rainfall hyetographs and corresponding surface runoff hydrographs, or they are based on an analysis of some (preferable physically based) parameters of the catchment. Maidment describes a methodology to derive the Unit Hydrograph based on a time-area diagram approach [Maidment, 1993c]. I derived a similar approach based on the PCRaster functions.

The concept assumes that a grid of local surface flow velocities can be derived. Local surface flow velocity may be approximated for each cell from an analysis of slope, land use and surface roughness associated with the individual cells. Estimates for surface velocity as a function of slope and land use are tabulated by various researchers and agencies (for examples see Kirpich [1940] and table 5.3). The example is based on these tabulations. Table 5.3

Woodland Pastures Cultivated Pavement

Approximate average velocities in ft/sec of runoff flow Slope Slope Slope 0–3% 4–7% 8 – 11 % Unconcentrated flow 0 – 1.5 1.5 – 2.5 2.5 – 3.25 0 – 2.5 2.5 – 3.5 3.5 – 4.25 0 – 3.0 3.0 – 4.5 4.5 – 5.5 0 – 8.5 8.5 – 13.5 13.5 - 17 Concentrated flow Use Manning formula

Slope 12 - % 3.25 4.25 5.5 17 -

Well defined channels Natural, not well 0-2 2-4 4-7 7defined, channels (Chow, 1988; Source: Drainage Manual, Texas HighWay Department, table VII, p II-28, 1970) The local travel time of each grid cell is determined by dividing by the local path length by this local surface flow velocity. This local travel time indicates the time an amount of surface water needs to travel through this grid cell. It is assumed that the parameters governing local surface flow velocity are independent of flow rate, water level and volume. The total travel time of the water located on a specific cell to arrive at the outlet of the catchment is now the sum of all the local travel times on the cells on the path from the specified cell to the outlet. The total travel time of each cell in the catchment to the outlet can be determined using the function ldddist (see chapter 4). The resultant map may be classified into zones, combining cells whose total travel time t falls in time interval T + dt. These zones, separated by isochrones, start contributing to the runoff at the outlet after the total time since the start of the storm exceeds the total travel time associated with this zone. One has to bear in mind that the unit hydrograph method is not a distributed dynamic model as defined in chapter 3. It describes the lumped dynamic behaviour of the outlet of the total catchment as a result of uniform static input. The resultant Unit Hydrograph can be used to create spatially lumped models which dynamically determine runoff for a given time series of excess precipitation. The following script can be used to determine the Unit Hydrograph: # Unit Hydrograph determination using local travel time concepts # Author: WPA van Deursen # Date: september 13, 1994 # Determine local surface flow velocity (meter/hour) based on values given in table 5.3 # (ft/sec) is multiplied by 1097.28 to obtain (meter/hour) localflowvelocityMap = 1097.28* lookupscalar(velocityTbl,landuseMap,slopeMap); # Determine local travel time based on local surface flow velocity localtraveltimeMap = 1.0/localflowvelocityMap; # Determine total travel time to catchment output totaltraveltimeMap = ldddist(lddMap,pits(lddMap),localtraveltimeMap);

Using the command unitHydrographtable = describe(totaltraveltimeMap,1)

yields tabular information on the distribution of cells in totaltraveltimeMap. The tabular information can be used to draw the histogram of the distribution of total travel times to outlet, which can be interpreted as the Unit Hydrograph resulting from a unit input of excess precipitation on the catchment. Figure 5.5a shows the totaltraveltimeMap for the example catchment, assuming a uniform localtravelTime of 1.0. Figure 5.5b shows the accompanying Unit Hydrograph.

One of the disadvantages of the original concepts of the Unit Hydrograph is that it assumes a uniform distribution of excess precipitation over the area. However, the above method of deriving the Unit Hydrograph allows for a non-uniform spatial distribution of excess precipitation. This spatial distribution may be the consequence of several soil or land use types in the area with different infiltration characteristics. This hydrograph can be obtained by creating a cross-tabulation of total travel time from each cell versus the amount of surface precipitation available in this cell. This can be obtained using the command unitHydrographtable=crosstbl(totaltraveltimeMap,excessprecipitationMap)

Excess precipitation may be obtained from methods such as the Curve Number approach as described in chapter 4.

Figure 5.5

5.5

a Travel time to outlet for example catchment b Resulting hydrograph

Dynamic surface water routing

In the previous section, the use of the Unit Hydrograph for the determination of the time series for runoff at the outlet of the catchment is discussed. The described model is a lumped model, which uses spatial distributed input data. However, the method used to find the hydrograph is not spatially distributed, since the described method does not yield distributed maps of lateral flow through the catchment. In this section distributed routing methods will be discussed. These routing methods allow for analysis of the lateral flow process in all elements of the topological network. Routing is the process of determining time and magnitude of a flow at several points in the channel. In a broad sense, it may be considered as the analysis of the lateral distribution of water in the hydrologic system with known inputs. Routing is the process of converting the input for a channel reach into outflow from that channel reach. It is a dynamic description: routing describes flow through a channel (or through a cell) as a function of time. Although in the literature a distinction is made between hydrologic routing, which is described as the methods to determine flow as a function of time only (lumped routing), and hydraulic routing (based on hydraulic laws and referred to as distributed routing), this distinction becomes vague if we apply hydrologic routing to a series of a large number of channel reaches. A more logical subdivision refers to methods used to describe the process. Hydraulic routing now refers to those methods that describe the routing process in terms of hydraulic laws, while hydrologic routing is based on an empirical relation between inflow and outflow. PCRaster allows for distributed routing, using the functions described in chapter 4. These functions allow for the construction of hydrologic as well as hydraulic routing procedures. Described in this section are several possibilities for using these functions for analysing routing processes.

Travel time routing Local travel time routing is an extension of the Unit Hydrograph methods described in section 5.4. For this Unit Hydrograph approach, it is assumed that the process of routing can be simplified and approximated by constant travel times through channel reaches. For each channel reach (i.e. raster cell), a local travel time can be determined, defined as the time needed to travel through this reach. Section 5.4 described an approach to determine local travel time for grid cells, which is extended here to include dynamic routing. No attention is paid

to infiltration approaches and the determination of excess precipitation, but it is assumed that the excess precipitation is randomly distributed over the area with intensities as given in figure 5.6. This very simple routing concept is implemented in the function traveltime. The redistribution of water is determined solely based on this local travel time, which determines the distance water travels during one model time step. The algorithms of the traveltime function are described in section 4.5.

Figure 5.6

a Random distribution of excess precipitation b Spatial and temporal distribution discharge

The following model script file is used to determine the outflow hydrograph of this situation, based on the travel time routing approach. # Routing using local travel time concepts # Author: WPA van Deursen # Date: september 13, 1994 initial localflowvelocityMap = 1097.28* lookupscalar(velocityTbl,landuseMap,slopeMap); localtraveltimeMap = cellsize(....)/localflowvelocityMap; timer ...........

dynamic SurfaceWater = ....; SurfaceWater,Discharge=traveltimestate,traveltimeflux(LddMap,SurfaceWater,localtraveltimeMap);

Level pool routing An improvement of the approach described in the previous section is to relate flow through a channel section to the amount of water available in the section. This requires a discharge-storage function, allowing discharge (flow) to be calculated as a function of storage. The general approach is to divide a river channel into river sections, and for the individual river sections outflow is described as a function of inflow and storage in the section. Conceptually, this is equal to a series of reservoirs, for which inflow into a reservoir consists of outflow of the previous reservoirs, and outflow (discharge) of each reservoir is described as a function of the amount of water in the reservoir. For linking this approach with raster GIS each grid cell in the river network is one of the reservoirs for which a discharge-storage function is defined. The local drain direction network defines the connection of each reservoir in the river network. Level pool routing is a procedure for calculating the outflow hydrograph from a reservoir with a horizontal water surface, given its inflow hydrograph and storage-outflow characteristics. The application of the procedure for hydrologic routing is limited to those situations where the assumption of a horizontal water surface does not introduce a too large error. This is the case in wide, deep river sections, where flow rates are low compared to storage values and there are no backwater effects. Since discharge from a section is described only as a function of storage of the reservoir, the approach does not allow for any backwater effects to be modelled. The approach is perfectly valid however, if there is an invariable relationship between storage S (or water level h) and discharge Q (see figure 5.7).

Figure 5.7

Invariable relationship between storage S and discharge Q

The PCRaster function to be used for this analysis is the function route. As described in section 4.5, the syntax of the function is: = routestate(,,)

and = routeflux(,,)

The FluxAmount entry is used to describe the storage-discharge relation. If the discharge is constant through time and independent of the storage, and assumed to be available in the map KnownFluxMap, the function call becomes StateMap,FluxMap = routestate,routeflux(LddMap,KnownFluxMap,PreviousState);

with StateMap FluxMap LddMap KnownFluxMap PreviousState

= resulting map with the state (amount stored in each grid cell) = resulting map with the calculated flux = input local drain direction map containing the river network = input flux map with known (constant) flux = input state map.

As explained in section 4.5.4, the function route evaluates the KnownFlux entry, and calculates the flux based on this entry. In the case of constant discharge, where the amount of water stored in the grid cell is sufficient to satisfy this flux, the resultant FluxMap will contain the same values as the KnownFluxMap. If the amount stored in the system is insufficient to satisfy this flux, the resultant FluxMap will contain the amount of discharge the storage was capable to supply. Dynamic behaviour of this routing procedure can be evaluated by assigning the resultant map to be input for the next time step, thus yielding a script file similar to # Routing example 1 # Dynamic routing using constant (predetermined) fluxes # Author: WPA van Deursen # Date: september 28, 1994 binding ModelArea = area.map; KnownFluxMap = constantflux.map; InitStateMap = initstate.map; LddMap = ldd.map; Stations = stations.map; Discharge = discharge.dat; areamap ModelArea; timer 1 10 1; initial State = InitStateMap; dynamic # allowing for additional water to be added to the routing process State = State + ...... # routing of water State,Flux=routestate,routeflux(LddMap,KnownFluxMap,State) # writing results for selected points report Discharge = timeoutput(Stations,Flux);

A storage-discharge behaviour (where discharge is a function of storage) may be constructed by replacing the constant KnownFlux with a relation describing flux as a function of storage. Assuming a known relation between storage and discharge given by the relation Q = aSb

(5.11)

with known values for a and b, the function call becomes StateMap,FluxMap = routestate,routeflux(LddMap, a*StateMap^b, StateMap);

with StateMap FluxMap LddMap a,b

= map with the state of the system = resulting map with the calculated flux = input local drain direction map containing the river network = (spatial distributed) constants

and the script file for dynamic modelling becomes # Routing example 2 # Dynamic routing using invariable storage-discharge relation # Author: WPA van Deursen # Date: september 28, 1994

binding ModelArea = area.map; InitStateMap = initstate.map; LddMap = ldd.map; Stations = stations.map; Discharge = discharge.dat; a = .... b = .... areamap ModelArea; timer 1 10 1; initial State = InitStateMap; dynamic # allowing for additional water to be added to the routing process State = State + ...... # routing of water State,Flux=routestate,routeflux(LddMap,a*State^b,State); # writing results for selected points report Discharge = timeoutput(Stations,Flux);

The storage-discharge relation can also be used to construct water level-discharge relations, which might represent Q-h rating curves for river sections. Assuming a rectangular cross section through the channel, water level is a linear function of storage h=c*S

(5.12)

A linear reservoir with discharge as a linear function of water level (Q = k * h) can thus be constructed by combining the two relations, yielding Q = k * h = k * c * S.

(5.13)

This function can be used for level pool routing through a rectangular channel, assuming a linear relation between water level and discharge, using the route-function State,Flux = routestate,routeflux(LddMap,k * c * State,State)

If the relation between channel reach storage and water level cannot be written as a formula, or the formula becomes too complex, the lookuptable function can be used. The function call becomes State,Flux= routestate,routeflux(LddMap,k * lookupscalar(leveltable,State),State)

This approach may be very useful when dealing with situations where runoff has to be routed through a channel with floodplains. The relation between water level and channel reach storage cannot be written as a simple continuous function, and a superior approach may be to construct a table relating water level to channel storage. # Routing example 3 # Dynamic routing using a level pool approach for channel reaches with floodplains # Author: WPA van Deursen # Date: september 28, 1994 binding ModelArea = area.map; InitStateMap = initstate.map; LddMap = ldd.map; Waterlevel = waterlevel.tbl; Stations = stations.map; Discharge = discharge.dat; k = .... areamap ModelArea;

timer 1 10 1; initial State = InitStateMap; dynamic # allowing for additional water to be added to the routing process State = State + ...... # routing of water State,Flux = routestate,routeflux(LddMap,k*lookupscalar(Waterlevel,State),State); # writing results for selected points report Discharge = timeoutput(Stations,Flux);

5.6

Advective transport, erosion and sedimentation

The route operators can be used to model processes of trans-port. Using these operators, the equations describing the transport mechanisms are defined by the user. If the trans-port equations are written as a function of another routing process, these operators can be used to implement advective transport. Advective transport can be defined as transport of material where a carrier flux is responsible for the transporting mechanism. Examples from physical geography are the transport of pollutants driven by water movement, but also the transport of sediment by water flow. As described in the previous sections, this movement of water can be described with the route-functions as CarrierState,CarrierFlux = routestate,route-flux(LddMap,.....,CarrierState)

in which the transport equations for water can be included. The transport of a pollutant (or sediment) as an effect of this water movement can be written as Transport of pollutant = f(CarrierFlux,...)

(5.14)

The combined definition of transport of water and pollutant is implemented with CarrierState,CarrierFlux = routestate,route-flux(LddMap,.......,CarrierState); PollutantState,PollutantFlux = routestate,routeflux(LddMap,f(CarrierFlux,...),PollutantState);

A simple example of the transport of salt dissolved in water can be simulated based on the concentration of salt in the carrier. The transport of salt can be simulated as moving the amount of water with the dissolved salt (of known concentra-tion) from one cell to the next. The following script file implements this mechanism. CarrierState = .....; PollutantState = .....; Concentration = PollutantState/CarrierState; CarrierState,CarrierFlux = routestate,route-flux(Lddmap,....,CarrierState); PollutantState,PollutantFlux =routestate,routeflux(LddMap, CarrierFlux*Concentrati-on,PollutantState);

The amount of salt transported is described as the concentra-tion of salt multiplied by the amount of water transported. The state of the salt component is determined as the result of moving this amount of salt through the LDD map.

5.7

Environmental modelling

The techniques described in the previous section can also be used for modelling other environmental processes. This section is devoted to ecological and environmental models. Here I focus only on processes of vegetation growth, competition and dispersal. Although it is clear that there are many more interesting processes in

environmental studies, the selected ones will give a good overview of the possibilities for integrating these models in the developed GIS. The concepts of mass balance spatial modelling as developed in chapter 3 and 4 are also valid for modelling vegetation growth and development [Jørgensen, 1988]. The compartments as described in chapter 4 are now used to store the number of individuals, amount of biomass of a certain species, percentage ground cover or some other parameter describing vegetation state. Incoming transports represent growth of the vegetation, while outgoing transports can be used for describing processes of mortality and decay of the vegetation. One of the simplest forms of modelling vegetation growth is by describing vegetation growth by an exponential growth curve. This model assumes unlimited resources and population growth (increase of number of individuals, vegetation mass or ground coverage) is a function of the present state of vegetation. The general formula for exponential growth can be written as: dB/dt = B*c-B*m

(5.15)

in which B c m

= scalar describing the state of the available vegetation = growing rate constant (determined by species and environment) = mortality rate or decay rate constant.

The systems diagram for such a model is given in figure 5.8 and a simple script file for the model reads: # Population dynamics example 1 # Exponential growth # Author: WPA van Deursen # Date: december 21, 1994 binding ModelArea = area.map; c1 = ....; m1 = ....; areamap ModelArea; timer 1 10 1; storage Population1; initial Population1 = ....; transport Growth1 to Population1: Growth1 = c1 * Population1 - m1 * Population1;

The exponential growth is a simplification. Vegetation growth will not occur uniformly over the area, but depends on availability of resources. This availability of resources can result in fast growing rates in areas with sufficient resources, and slow growing rates in areas with limited resources. To account for this, the concept of carrying capacity K is introduced. The carrying capacity K is defined as the state of the system for which the total growth of the population B*c equals the population mortality B*m. This yields the logistic growth equation dB/dt = rB(K-B)/K

(5.16)

in which r K

= intrinsic rate of natural increase = c - m = carrying capacity.

Clearly the carrying capacity of a population is dependent on available resources, such as water and nutrients, which are not evenly distributed over the area. As a result, the carrying capacity varies over space. This can be modelled by allowing K to be a spatial distributed parameter, whose value is determined by species characteristics and resources availability.

Figure 5.8

System diagram of simple ecologic model

Logistic growth can be the consequence of external factors, but typically growth is restricted because the vegetation is competing for a limited amount of resources. Both individuals of the same species and individuals of different species have to compete for the same limited amount of resources. The limited resources may include water and nutrients, but one of the major competition processes is competition for light. As vegetation grows, it develops a larger surface of leaves for intercepting light, thus creating a larger capability for growth and maintenance. However, this larger surface of leaves will shadow underlying leaves, and these leaves will no longer take part in the production of biomass. Other species developing in the neighbourhood of the plant will also attempt to grow large surfaces for intercepting light, and as these neighbours all develop, combined they will intercept almost all available light. The development of a certain individual will yield a relative advantage for this individual over other species in the capability of intercepting light, but at the same time it leads to a situation in which less of the same resource is available to be intercepted. The growth process for two populations in which a simple description of competition for limited resources is implemented reads: dB1/dt = r1 * B1 * (K1 - B1 - α12B2)/K1 and dB2/dt = r2 * B2 * (K2 - B2 - α21B1)/K2 where α12 and α21 are competition coefficients This yields the following script file # Population dynamics example 2 # Population competition # Author: WPA van Deursen # Date: december 21, 1994 binding ModelArea = area.map; K1Map = K1.map; K2Map = K2.map; r1 = ....; r2 = ....; alpha12 = ....; alpha21 = ....; areamap ModelArea; timer 1 100 1; storage Population1;

(5.17)

initial Population1 = 0.1; storage Population2; initial Population2 = 0.1; transport Growth1 to Population1: Growth1 = r1 * Population1 * (K1Map - Population1 - alpha12 * Population2)/K1Map; transport Growth2 to Population2: Growth2 = r2 * Population2 * (K2Map - Population2 - alpha21 * Population1)/K2Map;

In the above examples, a certain initial amount of biomass is available, and it is assumed that the process of vegetation growth is initiated with this amount. If the initial amount of a certain vegetation at a certain location is 0, or if all of the vegetation at a certain location has died off, the above model descriptions do not allow for spontaneous rise of new individuals to initiate the growth process. Some process of dispersion of the population through the area has to be incorporated to allow for colonization of locations previously not occupied. Applicable dispersion processes are seed distribution, clonal growth or vegetative reproduction. The following script introduces seed distribution as a random process to occupy empty regions. The amount of seed found at a location may be modelled as a function of (the inverse of) the distance to other locations occupied by the same species. For each location, the distance to the nearest location occupied by the species may be found using the spread function, and a general formulation of seed distribution may be Seed = f (...., spread(Population1, ..., ...), ...)

(5.18)

Some threshold of population state may be introduced, indicating that populations are only productive after a certain maturation. Seed = f (..., spread(Population1 gt 0.5, ...., ....), ....)

(5.19)

The growth of each population is now a combination of germination of seed and the growth as described in the previous example. The script file to implement this process is # Population dynamics example 3 # Population competition and seed distribution # Author: WPA van Deursen # Date: december 21, 1994 binding ModelArea = area.map; K1Map = K1.map; K2Map = K2.map; r1 = ....; r2 = ....; alpha12 = ....; alpha21 = ....; Thres1 = ....; Thres2 = ....; areamap ModelArea; timer 1 100 1; dynamic seed1 = ...... spread(Population1 gt Thres1, ....., .....).....; seed2 = ...... spread(Population2 gt Thres2, ....., .....).....; storage Population1; initial Population1 = 0.1; storage Population2; initial Population2 = 0.1; transport Growth1 to Population1: Growth1 = r1 * Population1 * (K1Map - Population1 - alpha12 * Population2)/ K1Map + ..... seed1....;

transport Growth2 to Population2: Growth2 = r2 * Population2 * (K2Map - Population2 - alpha21 * Population1)/ K2Map + .... seed2....;

The dispersion of seed can be modelled with other tools as well. If a predominant wind direction is responsible for dispersion into one direction, a LDD-map may be constructed as a preferred direction of seed dispersal. The accu and route functions are now available to describe the seed dispersal as a consequence of wind from a major direction. The same approach may be used for modelling catastrophic events such as forest fire, which is spread into the direction of the wind only.

6

CASE STUDIES

6.1

Introduction

This chapter presents several applications based on the PCRaster-software that have been developed over the last five years. My major objective in this research was not to build and test hydrological and ecological models, but as the development of the software progressed, the need for testing using more extended applications emerged. In this chapter, I want to illustrate the use and robustness of the PCRaster tools. The descriptions in this chapter are not meant to verify the validity of the results, and reference is made to the other publications on the models. It is through the processes of cooperation and mutual influence that both the PCRaster software and these application-projects got their final shape. In this chapter the prototypes and techniques described in the previous chapters have been incorporated into simulation models for hydrological and ecological purposes. Section 6.2 deals with the development and application of catchment scale water balance models used to analyse the sensitivity of the hydrologic regime of large river basins to climate change. These models, the RHINEFLOW class of PCRaster models, incorporate the soil water balance model and the steady flow accumulation of surface runoff as described in chapter 5. The RHINEFLOW model was used to investigate the effects of possible climate changes in the Rhine basin on the discharge of the river Rhine. A modified version of these models, the GBP model, incorporates the analysis of drought conditions by the aridity index described in section 5.2. This model was used for climate change research on the Ganges-Brahmaputra basin. Section 6.3 describes the development of an ecological simulation model. This PCRaster model, named CalGIS, simulates the competition between heather (Calluna) and grass (Deschampsia). The CalGIS model uses the mass balance approach for vegetation development. This model incorporates the inter-species competition model described in section 5.7. A disease in the heather population is introduced, which infects individuals randomly and contaminates the area in the neighbourhood of the infected locations, using the prototypes introduced in section 5.7. The study concerning the Rhine catchment is published in Kwadijk [1993] and as CHR/KHR report [CHR/KHR, 1995]. The Ganges-Brahmaputra study has been published as a Resource Analysis project report [Resource Analysis, 1994]. The research for the water balances was carried out in cooperation with Jaap Kwadijk of the Faculty of Physical Geography, University of Utrecht. The presentation of the research for the Calluna model has been modified from the publication 'Analysis of heathland dynamics using a spatial distributed GIS model' [Van Deursen and Heil, 1993]. This part of the study was carried out in cooperation with Gerrit Heil, currently working at Resource Analysis, Delft and the University of Utrecht.

6.2 Water balance studies of large river basins with respect to their sensitivity to climate changes

6.2.1 Introduction The world climate is expected to react to the enhanced green-house effect with changed patterns of precipitation and temperature distribution in time and space. Consequently, streamflow is also expected to change in volume and distribution over the year, giving major concerns to policy makers who are concerned with drought and flooding. Long-term strategies for future river manage-ment require quantitative information on these changes, for which hydrological models can often be important tools.

To date, outside the present study, no spatial distributed precipitation-runoff models have been developed to simulate the discharge of large river basins at the catchment size of the major tributaries. A spatial distributed water balance model, called RHINEFLOW, was developed as part of this study [Kwadijk, 1993]. RHINEFLOW aims at obtaining information for the Rhine catchment at a spatial resolution of the major tributaries and a temporal resolution of a month. Simultaneously the KHR/CHR (Internationale Kommission fur die Hydrologie des Rheingebietes, Internationale Commission de l'Hydrologie du bassin du Rhin) initiated a project to assess the impact of climate and land use changes on the discharge pattern of the river Rhine. Integrated studies analysing both physical impacts of climate change and the socio-economic water supply issues are currently being performed by the Dutch National Institute of Public Health and Environmental Protection (RIVM). One of these studies, called TARGETS (Tool to Assess Regional and Global Environmental and Health Targets for Sustainability - Rotmans et al. [1994], Hoekstra [1994]) is a detailed integrated study of the Indian subcontinent, with special focus on the Ganges-Brahmaputra basin. The RHINEFLOW water balance model was adapted to model this basin as well. This modified version of the RHINEFLOW model is called the GBP model. The questions that are discussed deal with the availability of water in the catchments, the temporal and spatial distribution of this availability and the changes in the availability as a result of climate change. Two important aspects of the water balance are the availability of water for agriculture and the runoff regime of the catchments. Climate change will have an impact on both these aspects. This section deals with the development of the water balance model and a case study of its application in the Rhine and the Ganges-Brahmaputra basins to simulate the reaction of the water balance of these catchments to climate change.

6.2.2 General model description The hydrological cycle of a drainage basin can be described as a series of storage compartments and flows. A water balance is often used as a framework to describe the transformation of input (precipitation) into output (runoff and evapotranspiration) through this cycle. The water balance of large river basins such as the GangesBrahmaputra basin and the Rhine basin can be described by six major (natural) storages and controls: The amount of precipitation and its spatial distribution. • The temperature distribution in the catchment, which mainly depends on the topography. This distribution forms the main control for the snow storage, snow-melt and potential evapotranspiration in the catchment. • Glacier and snow storage that gains water from precipitation and loses water to snow melt and ice melt. • Soil moisture storage/shallow ground water storage which gains water from the surplus of precipitation and loses water to evapotranspiration, to seepage to the deeper groundwater and to direct runoff. • Deeper groundwater storage which gains water from the soil water seepage and loses water to the river base flow. • The distribution of the land use and soil water storage capacity in the catchment, which control the actual evapotranspiration. The RHINEFLOW and GBP models are 3 compartment storage models. The storage compartments are snow storage, soil water storage and deep groundwater storage. Input is precipitation, which can fall either as snow or as rain. Figure 6.1 is a schematic overview of the model. Temporary snow storage for each grid cell is calculated by assuming that precipitation falls as snow when average monthly temperature is below a critical temperature for snow fall. Snow melt starts when the average monthly temperature is above this critical temperature for snow fall and increases with temperature above the critical temperature. Monthly evapotranspiration is determined using the temperature-dependent Thornthwaite-Mather [1957] equations (see also chapter 5.2). The amount of water stored in the soil is updated for each month. Each month the soil gains water from precipitation and snow melt, and each month the soil loses water due to evapotranspiration, seepage and direct runoff. Seepage and runoff occur if the sum of the amount of water already stored in the soil and the inputs from precipitation and snow melt exceeds the maximum water storage capacity of the soil. From the soil storage compartments, water flows directly into the river system (rapid runoff) or is delayed through the groundwater reservoir (delayed runoff).

Figure 6.1

Schematic overview of the RHINEFLOW and GBP models

The surplus of the soil water balance is separated into rapid runoff and seepage using a separation coefficient. This coefficient is used for calibration as described below. Seepage flows into the deeper groundwater reservoir. From this reservoir delayed runoff representing the baseflow of the river is calculated using a linear recession equation. The recession constant is also used for calibration. It is assumed that the base flow characteristics mainly depend on geohydrological properties of a catchment, and therefore will not alter under changing climatic conditions. Basin runoff is obtained from the grid-cell water balances by accumulating water production (rapid and delayed flow) for all cells in a (sub-)catchment. The usage of the accu-functions assumes that all water available for runoff leaves the catchment within a single time step (steady flow model). A monthly time step was found appropriate for both the Rhine and the Ganges-Brahmaputra basin. The model simulates average monthly runoff for a number of stations in the river basins. In addition it simulates spatially distributed data on monthly evapotranspiration, water availability and aridity conditions. A similar model concept has been applied to the river Nile [Conway, 1993]. All variables and parameters are stored in PCRaster. The model algorithms are implemented using the generic functions available in PCRaster [Van Deursen and Kwadijk, 1990]. Monthly storage, flows and losses are calculated for each raster-cell. The model output is in the form of raster maps and time series data. This model concept simplifies analysis of the model results in time and space. It also allows for rapid analysis of the effect of different spatially-distributed scenarios for precipitation and temperature changes. The maps for RHINEFLOW model were digitized and rasterised to a grid with a cell size of 3*3 km2 . Each of these raster cells in the data base represents one calculation element in the RHINEFLOW model and is the smallest element in the spatial connectivity analysis. For the Ganges-Brahmaputra basin a data set with a cell size of about 10*10 km2 is used. The choice of the spatial resolution is the result of several, mostly pragmatic, considerations. However, it is important to notice that the grid resolution used is certainly not the resolution at which the model results are reliable. The scale at which the models should be considered reliable is equivalent to several hundreds of cells. This is mainly the consequence of the data sets for climatic data, soil and land use. The considerations, which concern both accuracy of the input data and generalization problems related to converting new data into the database, are listed.

•

• • •

Topographical data was derived from maps with scales of 1:1,500,000 (Rhine catchment), 1:2,000,000 and 1:6,000,000 (Ganges-Brahmaputra catchment). On the maps of 1:1,500,000 a length of 2 mm represents a distance of 3 km and this length is assumed to be the maximum resolution of the spatial information of these maps. This resolution permits the accurate location of gauging stations along the rivers and the main tributaries. The model is designed for use on a personal computer. At time of the development of the model (1990), using this resolution a model run for 25 years took six hours on a PC (PC with 80386 processor and 8Mb RAM). The model is designed for the assessment of the impact of climate change. The changes in temperature and precipitation resulting from GCM's (Global Circulation Models) have been interpolated onto a grid of 0.5 degree latitude and 1.0 degree longitude using present day climate information (Climate Research Group University of East Anglia and Environmental Resources Limited, unpublished data). The used 3*3 km2 and 10*10 km2 grid are of higher resolution, and allow conversion of the scenario changes into the database without generalization problems.

The use of this grid size has some important limitations, namely: • Calculations of slope gradient, exposition and local drain direction from a DEM having a 3*3 km2 (or 10*10 km2 ) resolution do have a physical meaning, but it is not the usual one expected. These slopes show the directions of the change of the underlying elevation surface, and can be used to create the topological links in the local drain direction maps. The slopes cannot be expected to represent local slopes that can be measured in the field. Therefore, an accurate estimate for the process of overland flow is not possible with this modelling concept. Hence, flows like Hortonian overland flow, interflow and saturated overland flow are not incorporated into the model. The model has been developed to analyse the discharge of major rivers and their tributaries on a monthly time basis. Using this time basis and catchment scale, estimates of the individual contributions of different flows (saturated and Hortonian overland flow, interflow and groundwater flow) to the streamflow are difficult to make. • Detailed physically based models to determine snow melt and snow accumulation cannot be used since these models strongly depend on local slope exposition. • Since the river channels in the river basins are in general narrower than the grid size used, the drainage analysis does not make any statements about the nature of the channels (braided, meandering or anastomosing). • The model concepts used here do not allow for any divergent stream patterns in the river network. However, in the concept of a hydrological catchment, which is used here, it is assumed that all excess water available in the catchment will eventually flow to the outlet. This widely used concept does not allow for divergent streams either.

Calibration of the model Two criteria are used to calibrate the model. The first criterion is that the simulated annual runoff should correspond with the measured annual runoff, assuming a stable model. This assumption requires a zero change in average annual storage in glaciers, soil water and ground water. The second criterion is that the timing and magnitude of peak and low flows (on a monthly time basis) should be well represented. A measure to reflect the goodness of fit of the calculated hydrograph against the observed one is the coefficient of efficiency [Nash and Sutcliff, 1970]. A value of 1.0 for the coefficient of efficiency represents a perfect fit, values less than 0.0 mean that the average is a better representation than the model result. The coefficient of efficiency seems to reflect the general conclusions of model performance according to visual inspection fairly well [Bergström, 1976]. An optimal calibration and validation scheme includes a separation between dry and wet periods for calibration and validation purposes [Klemes, 1986b], which requires a long record of observations. One of the periods (either the dry period or the wet period) is used for calibrating the model, the other is used for validation purposes. To meet the first criterion, the model is run until the groundwater storage change and snow storage change over the year is zero. The snow module was calibrated so that snow cover duration was 12 months per year in cells identified as glaciers on land use maps. The accumulation and decay of the snow cover in these cells was kept in balance over the years. In all other cells the snow cover disappeared completely for at least one month per year.

The critical temperature for snow fall was kept at 0o Celsius. The procedure followed to meet the second criterion is to run the model, using the above snow module parameters, for 12 months to represent an average year. The separation coefficient and the recession coefficient are calibrated in simultaneously so that the model efficiency is maximised for this average year.

6.2.3 Modelling the effects of climate change on river discharge in the Rhine basin Hydrological setting of the Rhine basin In Western Europe the river Rhine is the most important river. Its basin of approximately 250,000 km2 stretches from the Alps to the North Sea. Two thirds of the basin is situated in Germany. The Alpine countries, of which Switzer-land is the most important, form 20% of the area. The river has the world's highest traffic density for inland waterways. Besides this navigation its economic importance is great because it is the major water supply for industrial, domestic and agricultural purposes. In addition, in the downstream region (The Netherlands) large amounts of Rhine water are used to prevent salt intrusion from the groundwater in the polders [CHR/KHR, 1976]. Possible future changes in discharge and river behaviour as a result of a climatic change may have large impact on the above mentioned water use.

Figure 6.2

a Hydrograph Rheinfelden b Hydrograph Rees

For the area upstream of Basel (Switzerland) the runoff regime is determi-ned by changes in the amount of snow storage and in the amount of water stored in the lakes. For the basin downstream of Basel these processes are of minor importance. In this part monthly runoff is mainly determined by groundwater recharge. The flow regime of the Rhine is characterized by the hydrographs of some gauging stations along the river (figure 6.2).

Data used for the RHINEFLOW model The RHINEFLOW model uses precipitation and temperature data obtained from the German and Swiss Meteorological offices (DWD and SMA). The set includes monthly areal precipitation since 1900 of the catchments of 18 segments of the river Rhine and of the main tributary catchments. Monthly temperature data was used for 27 stations. The temperature in a given raster cell is obtained from the temperature of the representative weather station and is corrected for the altitude of that cell with the use of elevation data from the Digital Elevation Model (DEM). As an additional source of information, average monthly evapotranspiration for different crop types for several stations in Germany (DWD) were obtained. This information was used for calibration and validation purposes. River discharge data was used to calibrate and to validate the model results against observed data. Monthly discharge data were obtained for seven gauging stations along the main river and for stations at the confluences of the main tributaries of the river Rhine. The time series cover periods ranging from 90 years (1870-1980) to 24 years (1956-1980). These data were obtained from the German Hydrological Office (BfG) and from the Swiss Hydrological Survey (BfL). Average monthly changes in snow water equivalents (SWE) for 30 mountain weather stations in the Alps were obtained from the geographical institute at the ETH (Switzerland) [Martinec et al. 1992]. Monthly changes in storage in natural and artificial lakes and in glacier storage in the Alpine area were taken from a study to the water balance of Switzerland [Schädler, 1985]. These data sets were also used for validation purposes. Land use data was derived from a land use map of the Rhine basin, scale 1:1,500,000 [CHR/KHR, 1976]. The map was digitized and rasterized for use in the GIS. A soil map, scale 1:1,500,000 [CHR/KHR, 1976] was digitized. The soil type map was relabelled into a maximum soil storage capacity map using relations derived by Groenendijk [1989]. Maximum soil water capacities range between 30 and 300 mm depending on soil texture, rooting depth of the vegetation, stoniness of the soil and depth of the lithic contact. The elevation data for the river basin was digitized from an elevation map, scale 1:1.500.000 [CHR/KHR, 1976]. This elevation data was interpolated to construct a DEM. Using this DEM the drainage pattern and drainage area of the river Rhine were determined (figure 6.3).

Calibration and validation of the RHINEFLOW model The model was calibrated using data for the period from November 1965 to October 1970 [Kwadijk, 1993]. This was a relatively wet period: the basin received 10-20% more precipitation than in an average year. The model was validated for the period from November 1956 to October 1980. Figure 6.4 shows the hydrographs for Rees and Rheinfelden. Rees represents the entire basin and Rheinfelden represents the Alpine area. The figure shows that the calculated discharge fluctuations represent the observed discharge over longer periods reasonably well. Analysis of the performance on monthly time basis in the Alpine basin shows that the discharge calculations are slightly too low during winter and summer and too high during autumn. The average calculated monthly evapotranspiration was compared with data on the average amount of evapotranspiration published by the DWD, Keller [1958], Baumgartner et al. [1983] and Schädler [1985]. The model results fit well with the data for the area downstream of Basel.

Figure 6.3

a Elavation map Rhine catchment b Simplified drainage pattern derived from elavation map c Observed drainage pattern

Figure 6.4

a Observed and simulated hydrograph Rheinfelden b Observed and simulated hydrograph Rees

Climate change and the effects on the discharge at the downstream part of the river Rhine As a first attempt to model the effects of climate change on the river Rhine, the discharge for a series of temperature and precipitation changes has been calculated [Kwadijk, 1993, Kwadijk and Van Deursen, 1993]. The results show the relative importance of these changes. Monthly discharges were calculated for a temperature rise of 0, 2 and 4 degrees Celsius combined with a precipitation change of -10, -20, 0, +10 and +20 percent, see table 6.1. Scenarios with a temperature decrease were not evaluated because they are not likely to occur. Based on these modified climate variables the monthly discharges of the river Rhine at the Dutch-German border (gauging station Lobith) were calculated with the RHINEFLOW model. The calculated discharges are compared with the results of a control run using the records of monthly temperature and precipitation for the period 19561980. Table 6.1

Scenarios analysed for the RHINEFLOW model temperature change 0o C 2o C precipitation change (%) -20 pm20t0 -10 pm10t0 pm10t2 0 p0t0 p0t2 10 pp10t0 pp10t2 20 pp20t0

4o C pm20t4 p0t4 pp20t4

Comparing model scenario discharge with observed present day discharge may give a false impression of the rate of change, since also the difference between the observed discharge and the calculated discharge of the

control run is included in the estimated change. In order to reduce the model error only the discharge changes estimated by the model have been considered. Consequently, the rate of change was calculated with: change ratio = (Qobs -(Qscen-Qctrl ))/Qobs

(6.1)

in which Qobs Qscen Qctrl

= the observed discharge (m3 /sec) = the scenario discharge as calculated by the model (m3 /sec) = the present day discharge calculated by the model (control run) (m3 /sec).

The results of discharge changes due to changes in temperature and preci-pitation are shown in figure 6.5. The major conclusion of the analysis is that both the annual and the seasonal discharge of the river Rhine are more sensitive to a change in precipitation than to change in temperature. The following conclusions for the discharge changes in the different seasons can be made [Kwadijk, 1993]: • • • • •

An increase in temperature has little effect on the discharge of the river Rhine. Discharge in all seasons, even in winter, is reduced. Summer and autumn discharges are the most sensitive, while winter discharge hardly changes. An increase in precipitation has a large increasing effect on the discharge in all seasons. The discharge in autumn is the most sensitive, while the discharge in spring is the least sensitive. A decrease in precipitation has a large decreasing effect on the discharge in all seasons. Again, the autumn discharge is the most sensitive. There is no difference in discharge reduction between the other seasons. A combination of increasing temperature and decreasing precipitation decrease gives an increasing reduction of the discharge in all seasons. The effect is largest for autumn and least for winter. A combination of temperature increase and precipitation increase has a relatively large increasing effect on the discharge in all seasons. Winter discharge is the most sensitive for this scenario, while summer discharge is the least affected.

Figure 6.5

Discharge change ratios due to changes in temperature and precipitation

6.2.4 Modelling the effects of climate change on river discharge in the GangesBrahmaputra basin Hydrological setting of the Ganges-Brahmaputra basin The Ganges flows from the Nepalese Himalayas through its Ganges plain in India and confluences with the Brahmaputra in Bangladesh. The catchment of the Ganges covers an area estimated as between 975 and 1,073 thousand square kilometres. The basin size of the Brahmaputra is estimated as between 530 and 938 thousand square kilometres [Gleick, 1993]. Average annual runoff of the Ganges is in the range of 15,000 m3 /sec and for the Brahmaputra this amounts 20,000 m3 /sec. Both river regimes are almost completely determined by the summer monsoon. During the monsoon the runoff in the downstream part of the Brahmaputra increases to 45,000 m3 /sec. During the dry period the discharge is reduced to 3,700 m3 /sec. The River Ganges produces 37,000 m3 /sec during the monsoon and 1,700 m3 /sec during the dry period. The river Ganges flows through the low land of India where much of its water is used for irrigation. The Brahmaputra flows from the dry high altitude plain in Tibet to Bangladesh. Upstream of Bangladesh only little of its water is used for agricultural purposes. The RHINEFLOW model described above was slightly modified for use in the Ganges-Brahmaputra basin. The new model is called the GBP model, and the modifications from the RHINEFLOW model are: • creating a new spatial database with input maps for the model; • creating a new climate database and allow for a modified definition of climate change scenarios; • determine new values for calibrated parameters and variables; and • include analysis of aridity and length of growing season. The GBP model incorporates the aridity index AI as described in chapter 5. To include these modifications required the change of approximately 10 lines of PCRaster code.

Climate data for the Ganges-Brahmaputra model The model for the Ganges-Brahmaputra uses precipitation and temperature data from the IIASA climate database. This database contains long-term monthly average climate data on a grid of 0.5*0.5 degree longitudelatitude from the reference period 1960-1980. In addition to this data the model uses time series of climate data from weather stations in the basin from the World Climate Disk (WCD-database) [CRU, 1992]. We used the IIASA grid data to calibrate the model. The model was validated using long-term time series for temperature and precipitation. The time series were derived by combining the average monthly data of the IIASA database with the month to month deviation for the period considered, using: Tx,y,t = Tx,y,t avg + dTx,y,t

(o C)

and Px,y,t = P x,y,t avg + Px,y,t avg *dPx,y,t /100 (mm) in which Tt avg = long-term average monthly temperature (o C) (IIASA database); dTt = temperature deviation from reference period temperature in month t at the representative station (o C) (CRU-WCD database); Pt avg = long-term average monthly precipitation (mm) (IIASA database); dPt = precipitation deviation (percentage) from the reference period precipitation in month t at the representative station (CRU-WCD database). Although this is a different method of deriving input data than used in the RHINEFLOW model, implementation required changing two lines of PCRaster code only.

Hydrological data River discharge data was used to calibrate and to validate the model results against observed data. Only limited data are available for river discharge in the Ganges-Brahmaputra catchment. Hydrological data in India is not freely accessible. To calibrate and validate the model we used time series of monthly discharge for the gauging stations at Farakka (India) and Bahadurabad (Bangladesh). The Farakka station represents the Ganges river, and Bahadurabad represents the Brahmaputra river. The data for these stations was obtained from the Global Runoff Data Centre (Koblenz, Germany). The time series cover the periods from 1949 to 1974 for the Farakka station and from 1969 to 1975 for the Bahadurabad station.

GIS database for the GBP model Land use data was derived from land use maps of India (National Atlas of India, scale 1: 2,000,000) and land use maps of China (Agricultural Atlas of China, scale 1:6.000.000). These maps were digitized and rasterized for use in the GIS. For the Ganges-Brahmaputra basin the resulting raster maps cover the area between 72o East, 34o North and 98o East, 20o North. Soil texture maps of India, scale 1: 2,000,000 (National Atlas of India) and China (Agricultural Atlas of China) were digitized. The texture classes were converted into maximum water storage capacity. The elevation data for both river basins were taken from the ETOPO5 database of the world (figure 6.6). Using this data the drainage pattern and drainage area of the basin of the rivers Ganges and Brahmaputra were determined.

Figure 6.6

a Elevation map of the Ganges-Brahmaputra basin b Ganges-Brahmaputra drainage net

Model results for the Ganges-Brahmaputra basin The GBP-model was calibrated using average year climate data and runoff data. The calibrated model was validated using time series runs. For the Ganges-Brahmaputra basin this time series covered the period 1969 to 1974 for the Farakka station and 1969 to 1975 for the Bahadurabad station. As a result of the war of liberation of Bangladesh (formerly East Pakistan), the hydrological data of 1971 is not reliable, so the validation period is relatively short. However, this is the only period for which a complete set of all input and control data series could be obtained. For the results of these runs see figure 6.7 and figure 6.8.

Figure 6.7

a Average mo nthly runoff and precipitation at Bahadurabad (Brahmaputra) b Average monthly runoff and precipitation at Farakka (Ganges)

The results of the calibration and validation procedure show that the model represents the average monthly flow of the Brahmaputra very well, both in the dry and in the wet season. Discharges at the Farakka station (Ganges) during the monsoon periods are well represented. However, during the dry season the model overestimates the runoff in the river Ganges. This can be explained by analysing the aridity index for the Ganges basin (see also figure 6.12). A substantial part of Ganges basin suffers from water shortages. During the dry months water is taken from the river to irrigate agricultural areas. The water used for irrigation does not return into the river but evaporates from the land under cultivation, and therefore the runoff in the river Ganges is reduced. In the Brahmaputra basin the drought problem is much smaller. Therefore less water is taken from the river and water losses are much smaller.

Figure 6.8

a Calculated and observed runoff Brahmaputra b Calculated and observed runoff Ganges

Climate change in the Ganges-Brahmaputra basin Climate change scenarios are described as changes in monthly precipitation and monthly mean temperatures. The climate change scenario represents possible changes in future climate if no climate change policies are adapted. Climate implications of greenhouse gas emissions from the IS92a scenario [IPCC, 1992] were studied with a simple aggregated climate model [Wigley and Raper, 1992]. The simulated increase in global mean temperature for the future projection year (2050) was scaled down by comparing the initial climatology from a GCM run with the average of monthly temperatures from the decade in a transient GCM run that yields the same global average temperature increase [Viner, 1994]. Monthly precipitation changes were simulated by comparing the initial GCM climatology to the same decade of the transient GCM run. The present study uses the downscaling result for the ECHAM model (Max Planck Institute, Hamburg, Germany).

Figure 6.9

a Mean monthly temperature Ganges-Brahmaputra (present and senario) b Mean monthly presipitation (present and scenario)

Figure 6.9a shows the mean monthly temperatures for the projection year 2050 for the whole GangesBrahmaputra basin. As shown in this figure, mean monthly temperature will increase by a total of 2.6 degrees until the projection year 2050. Figure 6.9b shows the mean monthly precipitation for the Ganges-Brahmaputra basin. From this figure, it is clear that changes in precipitation are highly correlated with the season. The start and end of the wet season are characterised by a decrease of precipitation, while during the wet season a large increase in precipitation is forecasted. The expected changes in precipitation and temperature are not uniformly distributed over the whole GangesBrahmaputra basin. In the Ganges basin the increase in mean temperature is 2.9 degrees, and for the Brahmaputra basin the average increase is 2.4 degrees. From the IS92a scenario it can be concluded that the Ganges basin is expected to be subject to larger changes in precipitation (figure 6.10a) and temperature (figure 6.10b) than the Brahmaputra basin.

Figure 6.10

a Mean monthly precipitation changes b Mean monthly temperature changes

Figure 6.11

a Present and scenario mean potential evapotranspiration b Present and scenario mean soil water storage c Present and scenario mean actual evapotranspiration

Changes in soil water storage, aridity index and evapotranspiration due to climate change As monthly evapotranspiration is closely correlated with the monthly mean temperatures, the changes in temperature will immediately affect the potential evapotranspiration. The results of the model for simulating the mean monthly evapotranspiration for the projection year 2050 are represented in figure 6.11. An average increase of potential evapotranspiration of 11.8 mm/month can be expected for the projection year 2050 from analysing the results of the scenario runs. The surplus of precipitation will ensure that the soils will be at maximum water holding capacity at the end of the wet season. Due to increased evapotranspiration, the amount of water stored in the soil at the end of the dry season will be decreased (figure 6.11b). As a result, a larger soil water deficiency at the end of the dry season will occur compared to the present situation. This deficiency in soil water means that the soil will not contain enough water to fulfil the demands of potential evapotranspiration completely. As a result of this water deficiency, the increase in monthly actual evapotranspiration is limited to about 7.6 mm/month as compared to an increase of potential evapotranspiration of 11.8 mm/month. As explained in chapter 5, the aridity index AI is an important indicator for water shortage and water demand. For the projection year 2050 the aridity index is given in figure 6.12 and table 6.1. From this figure, it can be concluded that the aridity situation will deteriorate as a result of climate change. Table 6.2 Brahmaputra

Average aridity index for the total catchment and the subcatchments of Ganges and

Total basin Ganges1) present situation 0.12 0.20 projection year 2050 0.15 0.24 1) Ganges Basin is the area upstream of gauging station at Farakka Brahmaputra basin is the area upstream of gauging station at Bahadurabad

Brahmaputra 1) 0.01 0.02

The aridity conditions in the Ganges basin are very different from the aridity conditions in the Brahmaputra basin. Analysing the maps of distribution of the aridity index yields the conclusion that the problem of aridity is much more pronounced in the Ganges basin than in the Brahmaputra basin. This may be explained by the fact that a large part of the Brahmaputra basin is in areas with high precipitation or at high elevation in the Himalayas, where temperatures are too low to cause a large potential evapotranspiration. The aridity indices for the different parts of the catchment are given in table 6.2.

Figure 6.12

a April aridity index (present situation) b April aridity index (scenario situation)

Changes in runoff due to climate change The (simulated) total runoff for the present situation and the projection year 2050 is given in table 6.3. The yearly cycle of the runoff for the selected projection year is given in figure 6.13. From these simulated runoff data it may be concluded that the runoff is not very sensitive to the scenario changes during the dry season (which are mainly characterised by changes in temperature), but is highly sensitive to the scenario changes during the wet season (which are mainly characterised by increase in both temperature and precipitation). Mean increase in runoff is 11.3 mm/month (projection year 2050). Maximum increase in runoff occurs during the months of July through September. Analysing the sensitivity of the subcatchments upstream of Farakka (Ganges) and upstream of Bahadurabad (Brahmaputra) yields the conclusion that the changes in the runoff of the Ganges are much more pronounced than the changes in runoff of the Brahmaputra. However, the timing of the peak flow of the Brahmaputra will be delayed by approximately one month, resulting in peak flows for both Ganges and Brahmaputra in August. Table 6.3

Total yearly runoff in mm for projection year 2050 Total basin Ganges1) present situation 678 450 projection year 2050 814 676 1) Ganges Basin is the area upstream of gauging station at Farakka Brahmaputra basin is the area upstream of gauging station at Bahadurabad

Brahmaputra 1) 899 924

Figure 6.13

a Present and scenario runoff at Farakka (Ganges) b Present and scenario runoff at Bahadurabad (Brahmaputra)

6.2.5 Conclusions and recommendations for the water balance studies The RHINEFLOW and GBP-model concepts have been found sufficiently robust to use for analysing the effects of climate change on the hydrologic situation in large river basins. Despite the limited data available for the Ganges-Brahmaputra basin, the model is capable of simulating the water balance under a wide range of climatic conditions. The RHINEFLOW-model can produce reliable results at the scale of a catchment of the major tributaries of the river Rhine. Although the tributaries have different climatic, topographical and land use properties the model performs well under the present-day climate conditions in these different physiographic settings. The model performs well for a (present day) variation in precipitation of 10-20%. To summarize, the model gives accurate quantitative description of the water balance compartments under the present-day conditions [Kwadijk, 1993]. The GBP-model slightly overestimates the runoff of the Ganges during the dry period. This is largely because actual irrigation practices are not incorporated in the model. An analysis of the agricultural water demand and data on the use of water for irrigation yields the conclusion that the amount of water used for irrigation accounts for the differences in simulated and measured runoff during the dry periods. The climate change scenarios used indicate a delay in the timing of the peak flow of the Brahmaputra. This may be very significant, because in that situation the timing of the peak flows of both the Ganges and Brahmaputra

will overlap. It can be concluded that both drought problems and flooding will increase. The increase in these problems is not uniformly distributed over the catchments. The model enables a detailed analysis of the position and timing of periods of drought and flooding. The RHINEFLOW model developed for the Rhine catchment proved to be robust enough to be used in the Ganges-Brahmaputra basin. The modifications necessary for the different inputs and controls (physiographic, climate etcetera) were easily incorporated into the model. After calibrating the modified model, the results for the Ganges-Brahmaputra basin proved to be reliable and useful. The model concept and the use of PCRaster for implementing the model proved to be flexible and robust. Another advantage of the models implemented in PCRaster is the capability to produce both maps of the spatial distribution and timeseries of the temporal distribution of the results. Theoretically, this allows for the analysis of the soil water balance and drought conditions in different sub regions and for the analysis of runoff at a large number of points along the river network. Such an analysis is important for the analysis of the aridity situation of smaller regions, which is very much controlled by the position of the regions within the catchment. However, since only few discharge data sets were available, the reliability of the model results within these subcatchments cannot be analysed. Therefore, the results produced by the model for these small catchments should be used with extreme care. Also, climate input is on a very coarse grid. Obviously, regional differences of climate and the related water availability within these grids are obscured. The water balance and runoff simulations of the Ganges-Brahmaputra basin with the climate change scenarios yield the conclusion that the two sub-basins (Ganges and Brahmaputra) have a very dissimilar reaction to climate change. There are two major reasons for this. First the inputs taken from the IS92a scenario are substantially different for each of the sub catchments. Secondly the reaction of the catchments is different. During the wet period the Ganges basin is characterised by a substantial increase in runoff, while the reaction of the Brahmaputra is less pronounced. During the dry period the Ganges basin is much more subject to drought conditions as is clear from the maps of the aridity index, a situation that will worsen as a result of climate change. The Brahmaputra basin is much less influenced by drought situations, both in present day and scenario situations. The increase of the aridity index for large parts of the Ganges basin will lead to a larger demand for water for agricultural uses. The model approach allows for an extension to incorporate agricultural yield response to changes in the water balance.

Acknowledgments We thank Dr. Schädler of the Bundesamt für Landeshydrologie und Geologie in Switzerland, Dr. Braun, Prof. Lang and Dr. Rohrer from the ETH in Zürich, Switzerland and Dr.Wildenhahn of the Bundesamt für Gewasserkunde in Germany and the German Meteorological Survey for supplying the hydrological and meteorolo-gical data for the RHINEFLOW model. Large parts of the research on the changes in runoff regime for the Ganges-Brahmaputra basin were carried out for the TARGETS project of the Dutch National Institute of Public Health and Environmental Protection (RIVM). Dr. Jan Rotmans, Arjen Hoekstra and Maarten Krol of the RIVM cooperated in the presented analysis of the changes in the runoff regime of the Ganges-Brahmaputra.

6.3

Analysis of heathland dynamics

6.3.1 Introduction In the Netherlands, many heathlands formerly dominated by Calluna vulgaris (L.) Hull - so called dry inland heathlands (Genisto-Callunetum) - have become dominated by grasses, especially by wavy hair grass (Deschampsia flexuosa (L.) Trin.). An evaluation of the extent of these changes in Dutch heathland using aerial photographs shows that more than 30% of former heathland has been replaced by grassland [Van Kootwijk and Van der Voet, 1990].

It has been suggested that eutrophication of heathlands may be a significant factor in the replacement of heather by grasses [De Smidt, 1979]. Field and laboratory experiments affirmed the importance of nutrients in heathlands [Aerts, 1989; Heil and Diemont, 1983]. However, during a heather beetle outbreak it was also observed that Calluna vulgaris is more severely affected by heather beetles in the more heavily nitrogen fertilized vegetation [Heil and Diemont, 1983]. This observation suggests that the replacement of Calluna vulgaris by grasses might not simply be due to the higher potential growth rate of the grasses under a higher level of nitrogen availability. Until recently, it was assumed that sulphur dioxide is the environmentally most damaging air pollutant in Western Europe. It has been suggested that the decline of many plant species in the Netherlands is caused by acidification of the environment [Van Dam et al., 1986]. Nowadays, however, the eutrophicating effects of atmospheric nitrogen have become more evident. Eutrophication largely results from ammonia/ammonium deposition, originating from the liquid manure used in great quantities in the intensive farming system in the Netherlands [Van Breemen et al., 1982; Buijsman et al., 1987]. Heathland has a strong filtering effect on ammonia/ammonium in which the canopy structure of the vegetation is an important factor [Heil et al., 1987; Bobbink et al., 1990]. It has been shown that increased nutrient availability results in a change in competition between Calluna and Deschampsia. Moreover, increased nutrient availability results in a higher nutrient content of the Calluna leaves [Aerts, 1989; Bobbink et al., 1990], and the results of rearing experiments show that increased nutrient content of the Calluna leaves results in better growth of the larvae of the heather beetle [Brunsting and Heil, 1985]. From these results it is hypothesized that outbreaks of this beetle are stimulated by nitrogen enrichment, and become more severe and occurring more frequently. Outbreaks of the heather beetle occur under certain conditions of food availability and of microclimatic conditions [De Smidt, 1977]. There are no outbreaks in young Calluna stands (< 5 years), because the percentage cover of the canopy of Calling must be more than approximately 50%. During an outbreak of this beetle plague Calluna plants die off almost completely over large areas [Berdowski and Zeilinga, 1987]. The opening up of the dwarf shrub canopy enhances the growth of grasses due to an elimination of the competition from Calluna. The deposition of atmospheric ammonia is not equally distributed but strongly depends on the number and size of local sources. Heil and Bobbink [1993] have developed a 1-dimensional simulation model, called 'Calluna', in which processes such as nitrogen cycling, heather beetle outbreaks and competition between plant species have been incorporated to describe the impact of atmospheric nitrogen deposition on the competition between Calluna and Deschampsia. The algorithms of this 1-dimensional model have been modified and used to build the spatial distributed CalGIS model.

6.3.2 Calluna model The model involves the growth of Calluna and Deschampsia. Growth is represented as the change in percentage cover of the plant species. Similar to the relation between biomass and diameter at breast height of trees a close relation between biomass and percentage cover of plant species exists, and is often used to determine the standing crop of the vegetation [Heil, 1984]. This relation is assumed linear for Calluna and Deschampsia and expressed as: B = C *β

(6.2)

where B C β

= dry weight standing crop per square metre; = percentage canopy cover of the species in a stand of vegetation per unit ground area; and = conversion factor for the individual species.

The conversion factors of Calluna and Deschampsia are different because of differences in the structure of the canopy. The Calluna canopy consists of woody parts, and brown and green leaves while the Deschampsia canopy consists of green and yellow leaves. The formulas for calculating the percentage cover for the two species are given by (see also section 5.7): SCt+1 = SCt + rC * SCt * (K - SCt - αcd * SDt ) /K

(6.3)

and SDt+1 = SDt + rD * SDt * (K - SDt -αdc * SCt )/K

(6.4)

where SC SD t rC rD αcd αdc K

= percentage cover Calluna = percentage cover Deschampsia = time = growth rate of Calluna = growth rate of Deschampsia = relative replacement rate of Deschampsia with respect to Calluna = relative replacement rate of Calluna with respect to Deschampsia = maximum percentage of cover (100%).

The growth rate of both Calluna and Deschampsia increase because of increased nitrogen availability. The growth rate of Deschampsia is significantly lower under nutrient-poor conditions. With increased levels of nutrient the growth rate of Deschampsia exceeds the rate of Calluna. During a heather beetle outbreak Calluna plants die off almost completely over large areas. When the heather canopy is abundant, the heather beetle affects Calluna randomly [Berdowski and Zeilinga, 1987]. It has been documented by Blankwaardt [1977] that heather beetle outbreaks have occurred with intervals of approximately 15 to 20 years when the atmospheric N deposition has been relatively low. Furthermore, it has been shown that there is a relationship between nutrient availability in the soil and nutrient content of the leaves of Calluna, which stimulates outbreaks of the heather beetle [Brunsting and Heil, 1985]. From the experiments a linear relationship has been estimated between the probability of occurrence of heather beetle outbreaks and nutrient availability (up to 100 kg N ha-1). This empirical relationship is used in the model to introduce outbreaks by a randomizer in combination with percentage cover of Calluna. Because of a heather beetle outbreak, the model reduces the percentage cover of Calluna to 1% of its original cover. Consequently, the nitrogen in the dead Calluna is passed into the soil compartment. Nitrogen cycling occurs between vegetation and soil compartments. In the model there is a nitrogen pool in Calluna, in Deschampsia and in the soil with three sub-compartments, the litter, fermentation and humus nitrogen pool. Litter is produced at different rates depending on plant species. Calluna has long-lived stems and the leaves die off in the second year [Aerts, 1989, Heil, 1984]. Although individual leaves of Deschampsia die off every year Deschampsia is considered an evergreen, because during one year two or more cohorts of leaves are formed [Aerts, 1993].

6.3.3 'CalGIS', the GIS implementation of the 'Calluna' model This section describes the implementation of the 'Calluna' model as described above using the modules from the PCRaster package. The first step when implementing a model such as 'Calluna' is the definition of the compartments (figure 6.14). The following compartments may be recognised: • The Calluna compartment, which contains the (spatially distributed) coverage of Calluna. • The Deschampsia compartment, which contains the (spatially distributed) coverage of Deschampsia. Combined with the Calluna compartment, this yields a value between 0 and 100, the percentage of the grid cell covered by the vegetation types. • The Beetle compartment. This compartment contains values of 1 for those locations where the beetle is present, and values of 0 if the beetle is not present. • The Litter, Ferment, Humus and Nutrient compartments, which store the different parts of the decomposition process. The nutrient compartment controls the growth rate of Calluna and Deschampsia. The combination of these compartments describes the state of the system at any time step in the model interval. The transition of the system into the state of the next time step is determined as a function of the initial state and the transports related to the compartments during the time step.

From figure 6.14, the following transports may be recognised: • C_growth, the growth of the Calluna compartment during the time step. This transport is controlled by the state of the compartments Calluna, Deschampsia and Nutrient. • D_growth, the growth of the Deschampsia compartment. This transport is determined by the amounts stored in the Calluna, Deschampsia and Nutrient compartments. The relation between the transports C_growth and D_growth describes the competition between the vegetation types. • C_death, the transformation of death Calluna into litter, which is controlled by the compartments Calluna and Beetle. • D_death, the transformation of dead Deschampsia into litter, controlled by the amount stored in the compartment Deschampsia. • B_growth, the flux that determines the growth of the beetle population. This growth is a stochastic function of existing beetle colonies and the amount of Calluna available for feeding. • B_death, the losses within the beetle colonies. Beetles are assumed to die if less than 50% of the grid cell is covered by Calluna. • Litter_to_Ferment, describing the flux (decay) of the litter compartment to fermentation compartment. • Ferment_to_Humus, describing the flux (decay) of ferment to the humus compartment. • Humus_to_Nutrient, describing the transformation of humus to the nutrient compartment • Atmospheric_Deposition, describing the deposition of nutrients from the atmosphere. This parameter is determined by the amount of nutrients in the atmosphere and is a direct result of emission and measures taken to reduce the amount of acidification. Implementing these transports in PCRaster yields the following script: storage Calluna; initial Calluna = 0.05; report Calluna.tim=summary(Calluna); storage Deschampsia; initial Deschampsia = 0.05; report Deschampsia.tim=summary(Deschampsia); storage Beetle; initial Beetle = 0; report Beetle.tim=summary(Beetle); storage Litter; initial Litter = 0; storage Ferment; initial Ferment = 0; storage Humus; initial Humus = 0; storage Nutrient; initial Nutrient = 0.5; report Nutrient.tim = summary(Nutrient); transport C_growth to Calluna; C_growth = (a*Nutrient + b)*Calluna*(100-Calluna-Deschampsia); transport D_growth to Deschampsia; D_growth = (c*Nutrient + d)*Deschampsia*(100-Calluna-Deschampsia); transport C_death from Calluna; C_death = if(Beetle=1 then 0.95*Calluna else f*Calluna); transport D_death from Deschampsia; D_death = g*Deschampsia;

Figure 6.14

System diagram of the CalGIS model

transport B_growth to Beetle; B_growth=if(normal()*windowtotal(Beetle,1500)>0.5 then 1.0 else 0.0); transport B_death from Beetle; B_death=if(Calluna < 50 then 1 else 0); transport Litter_to_Ferment from Litter to Ferment; Litter_to_Ferment=h*Litter;

transport Ferment_to_Humus from Ferment to Humus; Ferment_to_Humus=i*Ferment; transport Humus_to_Nutrient from Humus to Nutrient; Humus_to_Nutrient=k*Humus; transport Atmospheric_Deposition to Nutrient; Atmospheric_Deposition=......;

All the statements in this part of the model are self-explanatory, apart from the calculation of beetle growth (transport B_growth). Using the windowtotal function, a temporary map is created, which contains the sum of all the cells containing a beetle within a search radius of 1500 metres. This temporary map is multiplied with a map with random values between 0 and 1. For every cell in which the result is greater then 0.5 (meaning that there is at least one cell containing beetles within 1500 metre and a little bit of luck) a new beetle colony is introduced. The result is given in the transport 'B_growth'. Time series are gathered for the Calluna, Deschampsia, Beetle and Nutrient compartments using the statements report Calluna.tim=summary(Calluna); report Deschampsia.tim=summary(Deschampsia); report Beetle.tim=summary(Beetle); report Nutrient.tim=summary(Nutrient);

6.3.4 Results of the 'CalGIS' spatial simulation model Two nitrogen deposition scenarios have been applied to run the model, i.e. one relatively high (35 kg N ha-1yr1) and one relatively low (15 kg N ha-1yr-1) deposition scenario. The critical load for nitrogen deposition of heathland vegetation is approximately 20 kg N ha-1yr-1 [Heil and Bobbink, 1993], i.e. when the atmospheric deposition of nitrogen is more than approximately 20 kg N ha-1yr-1 the heathland vegetation will change relatively fast to a more or less permanent, grass dominated vegetation.

Figure 6.15

a Calluna cover for a scenario deposition of 15 kg N ha-1year-1 b Deschampsia cover for scenario deposition of 15 kg N ha-1year-1 c Competition between Calluna and Deschampsia

For the distribution of heathland vegetation all nutrient poor sandy soils were considered as potential habitat for heathland vegetation in the model. The results of the simulations with the two deposition scenarios show that Calluna vulgaris is still the dominant species over more than 90% of its potential distribution area, and it can compete successfully with Deschampsia flexuosa under an atmospheric deposition of 15 kg N ha-1yr-1 (see figure 6.15). Even heather beetle outbreaks did not diminish the competitive vigour of Calluna with respect to Deschampsia. Deschampsia dominates less than 5% of the whole area under this deposition scenario. However, under an atmospheric deposition of 35 kg N ha-1yr-1 the situation changes dramatically (see figure 6.16). Besides the more frequent and more intensive damage to Calluna by heather beetle infestation Deschampsia gradually replaces Calluna because the grass profits from the changed situation. Now Deschampsia dominates more than 25% of the whole area. In general, the results of the spatial calluna model - CalGIS - agree with the results of the 1-dimensional calluna model - Calluna. However, using spatial modelling, i.e. considering flight and infestation capacity of the heather beetle, the realism of simulating heathland dynamics has increased. Until now, the 1-dimensional model 'Calluna' could only present spatial results by suggesting that outbreaks of heather beetles wipe out the heather in one area, and do not affect the heather in a neighbouring area. The spatially distributed 'CalGIS' model is capable of describing the outbreaks of heather beetles pests and the effects on the Calluna vegetation in more detail.

Figure 6.16

a Calluna cover for a scenario deposition of 35 kg N ha-1year-1 b Deschampsia cover for scenario deposition of 35 kg N ha-1year-1 c Competition between Calluna and Deschampsia

The original simulation model in which processes such as nitrogen cycling, heather beetle outbreaks, competition between plant species are incorporated to establish the impact of atmospheric nitrogen deposition on the outcome of competition between Calluna and Deschampsia had already been used and constructed by Heil and Bobbink [1993]. However, the extension towards a spatially distributed version of the model yields results and insights that could not have been gained using the 1-dimensional version. In this case it was important to simulate discrete patches of heather between which there might be migration of the heather beetle. For this, the Netherlands could be divided in patches (cells) representing the potential distribution of heathland vegetation.

6.4

Concluding remarks

The simulation models described above show the applicability of the PCRaster system, which has been developed to be used as a generic tool for spatial dynamic modelling. The examples show simulation models from a variety of applications. Because of the high level of abstraction, the models are clearly readable, and the conversion of the RHINEFLOW model into the GBP model shows that the models can be easily modified and maintained. Although the models presented in this chapter are thoroughly tested and validated, the focus should be aimed at the usability of the developed tools. The results obtained by the models, however, also yield very interesting conclusions.

7

DISCUSSION AND RECOMMANDATIONS

7.1

Summary of research results

In the light of the results presented in chapters 4 through 6 this chapter gives answers to the research questions that were posed in chapter 1. The question to be answered was: •

Can we build a general purpose GIS with intrinsic dynamic modelling functionality, which can be used to develop, apply and evaluate models for a large number of environmental processes?

Related research questions were: •

What are the advantages and disadvantages of the different techniques available for linking GIS and dynamic models?

•

Can we classify the dynamic models currently used for physical geography, ecology and environmental issues into useful sets of approaches and processes?

•

Can we build general purpose tools to match these approaches and processes and are they capable of giving reasonable results for a variety of problems over a wide range of spatial scales?

•

Are these tools sufficiently robust to be given to GIS users who a) are not expert modellers, and/or b) have access to large amounts of pretty general data of mixed quality?

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For what kinds of dynamic modelling do they present a reasonable solution - where do they provide a useful supplement to existing methods?

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What should be the level of abstraction of these modules?

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Can we successfully model real-world problems in this GIS environment?

As discussed in chapter 2, a number of levels can be distinguished for linking GIS with dynamic models. Of these, the primitive linkages are currently the most widely used. Information exchange between model and GIS is through a process of ad-hoc data conversion (low level integration) or is obtained by the establishment of a common database structure supporting both GIS operations and model runs (medium level integration). These approaches have in common that they separate the task of database management (GIS) from process description (creation of dynamic model executable) and application of the system (running the model, forecasting, scenario analysis and decision making using the model). Current research and publications on the integration between GIS and dynamic models mainly focus on this low and medium level integration (eg. Steyaert and Goodchild [1994] and Goodchild et al. [1993]). The dynamic model itself remains external to the GIS and, as Maidment [1993a, 1993b] states: it does not seem productive to try to accomplish such simulations by intrinsic GIS functions, rather the simulation should be kept separate from the GIS and just use GIS as a spatial data source and in this sense, the coupling of GIS and hydrologic models seems to be a logical direction, rather than assuming that one can program hydrologic equations within GIS, a utility that will always be limited by the data model and operators available... However, the separation between the model and GIS is troublesome, and listed as disadvantages are: • the ad-hoc development of low level linkages is time consuming and has to be repeated for new versions of either the GIS or the model; • the low level linkage is hindered by redundancy and consistency problems due to the use of several instances of the same database;

• •

the medium level integration requires a relative open GIS structure, which is not available in most current GIS; and the model formulation remains at a relative low level.

The advantages of higher level integration become clear in this light. Although in theory these higher level integrations are handicapped by characteristics such as forcing the user into a straightjacket of model formulation and available numerical methods, the major advantage is the capability to build models relatively quickly and to be able to change and manipulate process descriptions, control parameters and sub-models at a high level. Several authors recognise these advantages of a higher level linkage [Kemp, 1993a, Fedra, 1993a]. Kemp [1993a] argues for the development of a next generation spatial modelling languages. She lists the strategy for the development of such a language as: • provide structures representing physical fields; • allow expression and manipulation of variables and data about continuous phenomena; • provide a syntax for incorporating primitive operations appropriate for environmental modelling with fields; • eliminate the necessity to consider the form of the spatial discretization whenever possible; and • the strategy should be capable of being incorporated into computer language implementations of environmental models. In general, the advantages of high level integration and the use of a spatial dynamic modelling language are listed as: • there is a full integration of GIS functionality for manipulation of input, results and formulation of the models; • no overhead for conversion between GIS and models and between individual models; • high level integration allows for rapid development of new models; and • high level integration allows for easy maintenance of models. The major disadvantages of a high level approach are: • the current generation of commercial GIS does not fully support dynamic spatial modelling; • investment in development of tools and functionality is high; • the user is forced into a straightjacket of model formulation and numerical methods; and • lack of specialist insight may yield invalid model concepts and formulations: the user is fully responsible for the model formulation. This thesis has dealt with the development of a prototype of such a spatial dynamic modelling language for a high level integration of environmental models in GIS and evaluates the use of the new language. High level languages provide a mechanism to express the problem in terms that conform with the concepts and ideas related to the subject. They allow for a compact expression of the problem by obscuring implementation details. By hiding details, they allow the user to maintain an overview of the problem, which helps prevent errors in developing solutions. The development of a high level language for modelling spatially distributed dynamic processes begins with a classification of approaches for this type of modelling into a limited number of categories, and subdivides each approach into separate generic tasks. Although the world of dynamic models for environmental processes is currently very dynamic, the methods can be standardised as using 1-dimensional, 2-dimensional and 3dimensional approaches. A very useful description for processes in these domains is by using Systems Analysis techniques for describing mass balances (chapter 4). This yields a framework of compartments for mass storage, interconnected with a network of fluxes, transporting mass from one compartment to another. This framework has been extended in this study to include spatial distributed compartments and transports, and to enable for the formulation of spatial distributed processes and internal redistribution of mass within the compartment. This framework yields a useful approach for describing a large number of processes encountered physical geography, hydrology and other environmental issues. The next step in the development of a high level language for spatial integration is the implementation of the generic concepts derived from the analysis of specific individual models into functions: modules that are capable of performing the generic tasks from which the total model can be constructed. The developed language implements all the functionality necessary for constructing compartments and creating the network of transports of mass between them.

The new language provides the functionality to create mass balance process models for physical geography. This means that they can be used to model processes related to water movement through the landscape, soil and pollutant movement, processes such as erosion and deposition and growth and distribution processes in ecosystems. The tools are very useful for implementing models of processes based on mass balance considerations, but as other terms become more important, the functionality may be insufficient. The detailed description of the process of infiltration and vertical water movement through the soil is based on a detailed simulation of the suction and changing permeability as a function of changing suction: generic tools may be inadequate for these processes. For these cases the system provides a mechanism for bypassing the System Analysis mass balance approach and implementing models based on mathematical formulation of the model. In addition, the database can be accessed using a library written in the C-language, and this mechanism enables the development of special purpose models. An example of this latter approach is the development of LISEM, a soil erosion model integrated in GIS [De Roo et al., 1994]. The developed language provides a powerful mechanism for implementing many different kinds of dynamic models in GIS. This raises questions about the robustness of the language in hands of non-experienced modellers. This problem of robustness has been addressed in several sections in the thesis. On the one hand, the tools are helpful in designing and structuring the model, and shield the user from the details of the implementation of the model. This enables the user to keep an overview of the model, instead of gaining insight in the number crunching of numerical solutions or the byte-level implications of changing model resolution. On the other hand, the user is still free to design whatever model he or she thinks is feasible and valid, and there is no mechanism or model expert knowledge in the system to point out weak or incorrect assumptions and methods. The language helps to design, to structure and to implement models, but it does not prevent the implementation of invalid model descriptions yielding incorrect results. Since the model is integrated in GIS, all common GIS-tools for deriving new digital maps from a combination of existing maps and interpolation of coarse point-data to a fine resolution data-set are available. The tools are integrated in a seamless way; extraction of necessary information can be done as part of the model description. Again a word of caution: the system cannot check whether relations assumed by the user have actual validity, and the responsibility for correctness is completely with the user.

The question whether we can actually analyse real world problems over a wide range of spatial scales with models built in this new GIS environment has been emphatically and positively answered in chapters 5 and 6. Important considerations relating to this question are which real world problems can be solved, and if there are problems that cannot. Obviously, there are many problems that are not suitable to be solved with this type of tools. First, the use of these tools assumes that the considered problem can be modelled mathematically. Many problems are too vague or do not contain deterministic parts that lend themselves for mathematical modelling. Second, the approach assumes that the mass balance approach is a valid approach to solve the problem. Many real world problems cannot be described as mass balance problems, because they involve the solution of choosing between multiple alternatives to establish multiple objectives. However, as can be illustrated with the examples in chapter 6, for a few of these problems the system provides a useful approach for simulating the processes that are important. The application of the tools is not only restricted to the processes of physical geography. As discussed in chapter 5 and 6, they also can be used for many different kinds of spatial problems, and the mass balance framework provides an approach that can be used for matters that are only slightly related to mass in a strict sense.

7.2 Recommendations for future research This research provided for a set of tools to make the integration of computational models in a spatial database system easier and more flexible. The spatial modelling language allows for the formulation of models for many environmental processes. It allows for structuring the problem and developing computer programs that can actually simulate the processes. Chapter 2 provided a list of principles that should guide model development. These principles are related to model building and structuring, as well as to data availability, accuracy and testing. Although the list is very clear in stating what a good model should be and should not be (it should not be more complex than it needs to be, it should be testable, it should be accurate), it does not give any guidelines for how to construct such a model. A model is never perfect, so there will be always the temptation to describe subprocesses in more detail, and increasing the complexibility of the model. Numerous examples can be given for models that try to model too much, try to describe too much detail of processes and need more data than is

feasible to collect. The common approach is starting to interpolate a few point data so that they cover a complete study area, or relate proxy estimates for important parameters to easy to measure data. This may easily lead to a model in which there is no balance between the complexity of the process description, the accuracy of the input data and the required accuracy of the final results of the model. Clearly this approach leads to a waste of (limited) resources, and yields a situation in which the application of models is not as beneficial as it could be. More research should be done regarding structuring the problem and balancing the complexity of the steps and components of the model building process. The PCRaster system provides interfaces for tools for advanced interpolation and error propagation. These tools allow for the evaluation of not only estimates of the expected results of spatial operations, but also for the analysis of the variance in the results. An interpolation of some physical field from point data can be accompanied by an estimate of the accuracy of the interpolation at each location in the physical field. However, the problem of propagation of errors or inaccuracies in the database through the process of dynamic modelling has barely been touched. Questions regarding the relation between support size of measurements and effective parameter values for models need more attention. A sound theoretical framework for calibrating and validating high resolution distributed models has not been set up yet. These are all question that should be addressed in the near future, to give spatial modelling a more sound scientific foundation.

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ACKNOWLEDGEMENTS This thesis would not have been finished without the continuing support and enthusiasm of my professor Peter Burrough. He not only guided me through the jungle of GIS, science and scientific writing, but he also managed to extent the STW project long enough so that, although I already quit my job at the University, I could finish this thesis. Many others were involved in the completion of this thesis. First, I want to thank Cees Wesseling. He provided me with deep insights in things such diverse as structured programming, zaalvoetbal, movies, bars and beers and lots of other items. Cees took the enormous task of explaining me why certain approaches I was very much in favour of could better be abandoned for simpler, more structured and definitely easier programmable approaches. Jaap Kwadijk learned me everything I know about mountain climbing and the geomorphology of the Rhine basin. His project on climate change in the Rhine basin has been the first project ever carried out in PCRaster. Without his ideas, problems and friendship, PCRaster would have been a different program. Where we, normal people, can see only mountains of problems, he keeps on telling us that these mountains are full of bushaltes large enough to put the tip of your toe on. He has the strange habit of asking me the most difficult questions while I am hanging in the ropes, 200 metres above the solid earth. Somehow, I learned to appreciate this behaviour. Matthuscka Persijn is thanked for all the programming work she had to do for this project. Whenever I had a, what I thought was a tremendous idea, Cees had to decide that it could be implemented, but Matthuscka was the one who had to program it. Of course, my ideas were not always that bright, and Cees was not always right in his judgements. For Matthuscka, there was nobody left to take care of the problems. Gerard Heuvelink, my roommate at the University explained me what random fields are, and he solved the statistical and mathematical problems of the complete department. The discussions we had on the deterministic nature of stochastic processes (or was it the other way around?) were very long and noisy, and still not finished. Bob MacMillan from Edmonton, Canada has been a great support in the early stages of the project. It is thanks to Bob that we have the largest number of pit removing options of any GIS available. The vakgroep Fysische Geografie has offered me a nice place to work, and there is a list of persons always willing to accompany me to pizza-dinners. These (former) colleagues and friends are Steven de Jong, Victor Jetten, Ad de Roo, Jos van Hees, Marc Bierkens, Ernst Jan Henkes, Edzer Pebesma, Hans Riezebos, Lodewijk Hazelhoff and many, many more. My current employer Resource Analysis is thanked for the time made available to finish this project. The colleagues of Resource Analysis supported me through this last year. Special thanks I owe to Jurgen Huizingh and Angelien van Boxtel, for not only sharing blessings and successes, but also sharing the problems and difficulties. Gerrit Heil is thanked for introducing me into ecological modelling, discussing science and careers and commenting on the draft versions of the thesis. Hoewel de steun van alle genoemde (en een heleboel niet genoemde) mensen onmisbaar is geweest voor het overleven van de jaren waarin ik dit proefschrift heb geschreven, is er een groep die ook onmisbaar is geweest in alle jaren daarvoor. Riet, Miek, Pau, kinderen, Lied, Ciel, Bert, kinderen, Miech, Ditte, Tijs, Hans, Jack, Jaap, Maart, Eliz, kind, Koen, Suzan, kinderen, Koos bedankt voor alle steun, interresse en gezelligheid. Tenslotte wil ik Marice bedanken. Zowel inhoudelijk als voor de uiteindelijke uitvoering (als bij het wandelen) heeft zij mij meer dan eens op het juiste pad teruggezet. Het is fijn iemand in de buurt te hebben die de stress van het promoveren van heel dichtbij kent. Overigens, gefeliciteerd met je overwinning...

CURRICULUM VITAE Ik ben geboren op 10 februari 1960 in Zeist. In juni 1978 behaalde ik het diploma Atheneum-B aan de scholengemeenschap 'De Breul' te Zeist. In 1979 begon ik met de studie Cultuurtechniek in Wageningen. Hiervoor behaalde ik in 1987 mijn doctoraal diploma. De belangrijkste vakken van de doctoraalstudie waren Cultuurtechniek, Afvoerhydrologie en Informatica. In het kader van deze studie heb ik een zes maands stage gedaan bij de Klamath Indian tribe in de Verenigde Staten. Vanaf 1 maart 1988 ben ik als toegevoegd onderzoeker aangesteld aan de vakgroep Fysische Geografie van de Universiteit van Utrecht. De weerslag van het grootste deel van dit werk is te vinden in dit proefschrift. Naast het schrijven van dit proefschrift heb ik mij bezig gehouden met het GIS-onderwijs, en ben ik 3 maanden naar Canada geweest voor het bouwen van een bodem informatie systeem. Vanaf mei 1991 ben ik werkzaam bij Resource Analysis in Delft.